diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 6183638ab587e..65b34fe157b71 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -6890,11 +6890,6 @@ def interpolate(
         axis = self._get_axis_number(axis)
         index = self._get_axis(axis)
 
-        if isinstance(self.index, MultiIndex) and method != "linear":
-            raise ValueError(
-                "Only `method=linear` interpolation is supported on MultiIndexes."
-            )
-
         # for the methods backfill, bfill, pad, ffill limit_direction and limit_area
         # are being ignored, see gh-26796 for more information
         if method in ["backfill", "bfill", "pad", "ffill"]:
@@ -6913,39 +6908,14 @@ def interpolate(
         else:
             df = self.T
 
-        if self.ndim == 2 and np.all(self.dtypes == np.dtype(object)):
+        if np.all(self.dtypes == np.dtype(object)):
             raise TypeError(
                 "Cannot interpolate with all object-dtype columns "
                 "in the DataFrame. Try setting at least one "
                 "column to a numeric dtype."
             )
 
-        if method == "linear":
-            # prior default
-            index = np.arange(len(df.index))
-        else:
-            methods = {"index", "values", "nearest", "time"}
-            is_numeric_or_datetime = (
-                is_numeric_dtype(index.dtype)
-                or is_datetime64_any_dtype(index.dtype)
-                or is_timedelta64_dtype(index.dtype)
-            )
-            if method not in methods and not is_numeric_or_datetime:
-                raise ValueError(
-                    "Index column must be numeric or datetime type when "
-                    f"using {method} method other than linear. "
-                    "Try setting a numeric or datetime index column before "
-                    "interpolating."
-                )
-
-        if isna(index).any():
-            raise NotImplementedError(
-                "Interpolation with NaNs in the index "
-                "has not been implemented. Try filling "
-                "those NaNs before interpolating."
-            )
-        data = df._mgr
-        new_data = data.interpolate(
+        new_data = df._mgr.interpolate(
             method=method,
             axis=self._info_axis_number,
             index=index,
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index e2a778f729470..31b38941c0153 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1104,13 +1104,10 @@ def interpolate(
                 coerce=coerce,
                 downcast=downcast,
             )
-        # validate the interp method
-        m = missing.clean_interp_method(method, **kwargs)
 
         assert index is not None  # for mypy
-
         return self._interpolate(
-            method=m,
+            method=method,
             index=index,
             axis=axis,
             limit=limit,
@@ -1178,6 +1175,9 @@ def _interpolate(
         inplace = validate_bool_kwarg(inplace, "inplace")
         data = self.values if inplace else self.values.copy()
 
+        # validate the interp method and get xvalues
+        method, xvalues = missing.clean_interp_method(method, index, **kwargs)
+
         # only deal with floats
         if not self.is_float:
             if not self.is_integer:
@@ -1187,11 +1187,6 @@ def _interpolate(
         if fill_value is None:
             fill_value = self.fill_value
 
-        if method in ("krogh", "piecewise_polynomial", "pchip"):
-            if not index.is_monotonic:
-                raise ValueError(
-                    f"{method} interpolation requires that the index be monotonic."
-                )
         # process 1-d slices in the axis direction
 
         def func(yvalues: np.ndarray) -> np.ndarray:
@@ -1200,7 +1195,7 @@ def func(yvalues: np.ndarray) -> np.ndarray:
             # should the axis argument be handled below in apply_along_axis?
             # i.e. not an arg to missing.interpolate_1d
             return missing.interpolate_1d(
-                xvalues=index,
+                xvalues=xvalues,
                 yvalues=yvalues,
                 method=method,
                 limit=limit,
diff --git a/pandas/core/missing.py b/pandas/core/missing.py
index d8671616f944e..cff663912acbe 100644
--- a/pandas/core/missing.py
+++ b/pandas/core/missing.py
@@ -2,7 +2,7 @@
 Routines for filling missing data.
 """
 
-from typing import Any, List, Optional, Set, Union
+from typing import TYPE_CHECKING, Any, List, Optional, Set, Tuple, Union
 
 import numpy as np
 
@@ -12,16 +12,22 @@
 from pandas.core.dtypes.cast import infer_dtype_from_array
 from pandas.core.dtypes.common import (
     ensure_float64,
+    is_datetime64_any_dtype,
     is_datetime64_dtype,
     is_datetime64tz_dtype,
     is_integer_dtype,
+    is_numeric_dtype,
     is_numeric_v_string_like,
     is_scalar,
     is_timedelta64_dtype,
     needs_i8_conversion,
 )
+from pandas.core.dtypes.generic import ABCMultiIndex
 from pandas.core.dtypes.missing import isna
 
+if TYPE_CHECKING:
+    from pandas import Index
+
 
 def mask_missing(arr, values_to_mask):
     """
@@ -94,7 +100,16 @@ def clean_fill_method(method, allow_nearest=False):
     return method
 
 
-def clean_interp_method(method: str, **kwargs) -> str:
+def clean_interp_method(
+    method: str, index: "Index", **kwargs
+) -> Tuple[str, np.ndarray]:
+    """
+    Validate Index and order keyword for interpolation methods.
+
+    Returns
+    -------
+    tuple of str, np.ndarray
+    """
     order = kwargs.get("order")
     valid = [
         "linear",
@@ -120,8 +135,49 @@ def clean_interp_method(method: str, **kwargs) -> str:
         raise ValueError("You must specify the order of the spline or polynomial.")
     if method not in valid:
         raise ValueError(f"method must be one of {valid}. Got '{method}' instead.")
+    if method in ("krogh", "piecewise_polynomial", "pchip"):
+        if not index.is_monotonic:
+            raise ValueError(
+                f"{method} interpolation requires that the index be monotonic."
+            )
+    elif method == "time":
+        if not getattr(index, "is_all_dates", None):
+            raise ValueError(
+                "time-weighted interpolation only works "
+                "on Series or DataFrames with a DatetimeIndex"
+            )
+        method = "values"
 
-    return method
+    if method == "linear":
+        xvalues = np.arange(len(index))
+    else:
+        if isinstance(index, ABCMultiIndex):
+            raise ValueError(
+                "Only `method=linear` interpolation is supported on MultiIndexes."
+            )
+
+        methods = {"index", "values", "nearest", "time"}
+        is_numeric_or_datetime = (
+            is_numeric_dtype(index.dtype)
+            or is_datetime64_any_dtype(index.dtype)
+            or is_timedelta64_dtype(index.dtype)
+        )
+        if method not in methods and not is_numeric_or_datetime:
+            raise ValueError(
+                "Index column must be numeric or datetime type when "
+                f"using {method} method other than linear. "
+                "Try setting a numeric or datetime index column before "
+                "interpolating."
+            )
+        if isna(index).any():
+            raise NotImplementedError(
+                "Interpolation with NaNs in the index "
+                "has not been implemented. Try filling "
+                "those NaNs before interpolating."
+            )
+        xvalues = index.values
+
+    return method, xvalues
 
 
 def find_valid_index(values, how: str):
@@ -195,16 +251,6 @@ def interpolate_1d(
     if valid.all():
         return yvalues
 
-    if method == "time":
-        if not getattr(xvalues, "is_all_dates", None):
-            # if not issubclass(xvalues.dtype.type, np.datetime64):
-            raise ValueError(
-                "time-weighted interpolation only works "
-                "on Series or DataFrames with a "
-                "DatetimeIndex"
-            )
-        method = "values"
-
     valid_limit_directions = ["forward", "backward", "both"]
     limit_direction = limit_direction.lower()
     if limit_direction not in valid_limit_directions:
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 71ffdcbd40fe7..ad9bf8c00f0ac 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -40,6 +40,7 @@
 from pandas.core.dtypes.cast import (
     convert_dtypes,
     maybe_cast_to_extension_array,
+    maybe_downcast_to_dtype,
     validate_numeric_casting,
 )
 from pandas.core.dtypes.common import (
@@ -92,6 +93,7 @@
 from pandas.core.indexes.timedeltas import TimedeltaIndex
 from pandas.core.indexing import check_bool_indexer
 from pandas.core.internals import SingleBlockManager
+import pandas.core.missing as missing
 from pandas.core.sorting import ensure_key_mapped
 from pandas.core.strings import StringMethods
 from pandas.core.tools.datetimes import to_datetime
@@ -2237,6 +2239,58 @@ def quantile(self, q=0.5, interpolation="linear"):
             # scalar
             return result.iloc[0]
 
+    @doc(NDFrame.interpolate)
+    def interpolate(
+        self,
+        method: str = "linear",
+        axis: Axis = 0,
+        limit: Optional[int] = None,
+        inplace: bool = False,
+        limit_direction: str = "forward",
+        limit_area: Optional[str] = None,
+        downcast: Optional[str] = None,
+        **kwargs,
+    ) -> Optional["Series"]:
+        inplace = validate_bool_kwarg(inplace, "inplace")
+
+        axis = self._get_axis_number(axis)
+
+        # for the methods backfill, bfill, pad, ffill limit_direction and limit_area
+        # are being ignored, see gh-26796 for more information
+        if method in ["backfill", "bfill", "pad", "ffill"]:
+            return self.fillna(
+                method=method,
+                axis=axis,
+                inplace=inplace,
+                limit=limit,
+                downcast=downcast,
+            )
+
+        # validate the interp method and get xvalues
+        method, xvalues = missing.clean_interp_method(method, self.index, **kwargs)
+
+        arr = missing.interpolate_1d(
+            xvalues,
+            self.values,
+            method=method,
+            limit=limit,
+            limit_direction=limit_direction,
+            limit_area=limit_area,
+            bounds_error=False,
+            **kwargs,
+        )
+
+        if downcast is not None:
+            arr = maybe_downcast_to_dtype(arr, dtype=downcast)
+
+        result = self._constructor(arr, index=self.index, fastpath=True)
+
+        if inplace:
+            self._update_inplace(result)
+            return None
+        else:
+            return result.__finalize__(self, method="interpolate")
+
     def corr(self, other, method="pearson", min_periods=None) -> float:
         """
         Compute correlation with `other` Series, excluding missing values.