diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 8c57496e092c4..ea085b3d1f6ab 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -106,6 +106,7 @@
 
 from pandas.core import (
     algorithms,
+    missing,
     nanops,
 )
 from pandas.core.algorithms import (
@@ -142,6 +143,7 @@
 from pandas.tseries import frequencies
 
 if TYPE_CHECKING:
+    from pandas import Index
     from pandas.core.arrays import (
         DatetimeArray,
         PeriodArray,
@@ -2228,6 +2230,46 @@ def copy(self, order: str = "C") -> Self:
         new_obj._freq = self.freq
         return new_obj
 
+    def interpolate(
+        self,
+        *,
+        method,
+        axis: int,
+        index: Index | None,
+        limit,
+        limit_direction,
+        limit_area,
+        fill_value,
+        inplace: bool,
+        **kwargs,
+    ) -> Self:
+        """
+        See NDFrame.interpolate.__doc__.
+        """
+        # NB: we return type(self) even if inplace=True
+        if method != "linear":
+            raise NotImplementedError
+
+        if inplace:
+            out_data = self._ndarray
+        else:
+            out_data = self._ndarray.copy()
+
+        missing.interpolate_array_2d(
+            out_data,
+            method=method,
+            axis=axis,
+            index=index,
+            limit=limit,
+            limit_direction=limit_direction,
+            limit_area=limit_area,
+            fill_value=fill_value,
+            **kwargs,
+        )
+        if inplace:
+            return self
+        return type(self)._simple_new(out_data, dtype=self.dtype)
+
 
 # -------------------------------------------------------------------
 # Shared Constructor Helpers
diff --git a/pandas/core/arrays/numpy_.py b/pandas/core/arrays/numpy_.py
index 702180b5d779a..113f22ad968bc 100644
--- a/pandas/core/arrays/numpy_.py
+++ b/pandas/core/arrays/numpy_.py
@@ -19,6 +19,7 @@
 
 from pandas.core import (
     arraylike,
+    missing,
     nanops,
     ops,
 )
@@ -33,9 +34,12 @@
         Dtype,
         NpDtype,
         Scalar,
+        Self,
         npt,
     )
 
+    from pandas import Index
+
 
 # error: Definition of "_concat_same_type" in base class "NDArrayBacked" is
 # incompatible with definition in base class "ExtensionArray"
@@ -220,6 +224,43 @@ def _values_for_factorize(self) -> tuple[np.ndarray, float | None]:
             fv = np.nan
         return self._ndarray, fv
 
+    def interpolate(
+        self,
+        *,
+        method,
+        axis: int,
+        index: Index | None,
+        limit,
+        limit_direction,
+        limit_area,
+        fill_value,
+        inplace: bool,
+        **kwargs,
+    ) -> Self:
+        """
+        See NDFrame.interpolate.__doc__.
+        """
+        # NB: we return type(self) even if inplace=True
+        if inplace:
+            out_data = self._ndarray
+        else:
+            out_data = self._ndarray.copy()
+
+        missing.interpolate_array_2d(
+            out_data,
+            method=method,
+            axis=axis,
+            index=index,
+            limit=limit,
+            limit_direction=limit_direction,
+            limit_area=limit_area,
+            fill_value=fill_value,
+            **kwargs,
+        )
+        if inplace:
+            return self
+        return type(self)._simple_new(out_data, dtype=self.dtype)
+
     # ------------------------------------------------------------------------
     # Reductions
 
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 7c5d686d96939..696884e344e40 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1394,18 +1394,16 @@ def interpolate(
             )
 
         refs = None
+        arr_inplace = inplace
         if inplace:
             if using_cow and self.refs.has_reference():
-                data = self.values.copy()
+                arr_inplace = False
             else:
-                data = self.values
                 refs = self.refs
-        else:
-            data = self.values.copy()
-        data = cast(np.ndarray, data)  # bc overridden by ExtensionBlock
 
-        missing.interpolate_array_2d(
-            data,
+        # Dispatch to the PandasArray method.
+        # We know self.array_values is a PandasArray bc EABlock overrides
+        new_values = cast(PandasArray, self.array_values).interpolate(
             method=method,
             axis=axis,
             index=index,
@@ -1413,8 +1411,10 @@ def interpolate(
             limit_direction=limit_direction,
             limit_area=limit_area,
             fill_value=fill_value,
+            inplace=arr_inplace,
             **kwargs,
         )
+        data = new_values._ndarray
 
         nb = self.make_block_same_class(data, refs=refs)
         return nb._maybe_downcast([nb], downcast, using_cow)
@@ -2262,18 +2262,22 @@ def interpolate(
         if method == "linear":  # type: ignore[comparison-overlap]
             # TODO: GH#50950 implement for arbitrary EAs
             refs = None
+            arr_inplace = inplace
             if using_cow:
                 if inplace and not self.refs.has_reference():
-                    data_out = values._ndarray
                     refs = self.refs
                 else:
-                    data_out = values._ndarray.copy()
-            else:
-                data_out = values._ndarray if inplace else values._ndarray.copy()
-            missing.interpolate_array_2d(
-                data_out, method=method, limit=limit, index=index, axis=axis
+                    arr_inplace = False
+
+            new_values = self.values.interpolate(
+                method=method,
+                index=index,
+                axis=axis,
+                inplace=arr_inplace,
+                limit=limit,
+                fill_value=fill_value,
+                **kwargs,
             )
-            new_values = type(values)._simple_new(data_out, dtype=values.dtype)
             return self.make_block_same_class(new_values, refs=refs)
 
         elif values.ndim == 2 and axis == 0: