diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index ba5334b2f4fa8..2f112990cab55 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -279,6 +279,7 @@ Deprecations
 - Deprecated logical operation between two non boolean :class:`Series` with different indexes always coercing the result to bool dtype. In a future version, this will maintain the return type of the inputs. (:issue:`52500`, :issue:`52538`)
 - Deprecated :func:`value_counts`, use ``pd.Series(obj).value_counts()`` instead (:issue:`47862`)
 - Deprecated :meth:`Series.first` and :meth:`DataFrame.first` (please create a mask and filter using ``.loc`` instead) (:issue:`45908`)
+- Deprecated :meth:`Series.interpolate` and :meth:`DataFrame.interpolate` for object-dtype (:issue:`53631`)
 - Deprecated allowing ``downcast`` keyword other than ``None``, ``False``, "infer", or a dict with these as values in :meth:`Series.fillna`, :meth:`DataFrame.fillna` (:issue:`40988`)
 - Deprecated allowing arbitrary ``fill_value`` in :class:`SparseDtype`, in a future version the ``fill_value`` will need to be compatible with the ``dtype.subtype``, either a scalar that can be held by that subtype or ``NaN`` for integer or bool subtypes (:issue:`23124`)
 - Deprecated behavior of :func:`assert_series_equal` and :func:`assert_frame_equal` considering NA-like values (e.g. ``NaN`` vs ``None`` as equivalent) (:issue:`52081`)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 6e71f32336546..711e552f262ac 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -7882,6 +7882,18 @@ def interpolate(
                 FutureWarning,
                 stacklevel=find_stack_level(),
             )
+        elif np.any(obj.dtypes == object):
+            # GH#53631
+            if not (obj.ndim == 2 and np.all(obj.dtypes == object)):
+                # don't warn in cases that already raise
+                warnings.warn(
+                    f"{type(self).__name__}.interpolate with object dtype is "
+                    "deprecated and will raise in a future version. Call "
+                    "obj.infer_objects(copy=False) before interpolating instead.",
+                    FutureWarning,
+                    stacklevel=find_stack_level(),
+                )
+
         if method not in fillna_methods:
             axis = self._info_axis_number
 
diff --git a/pandas/tests/copy_view/test_interp_fillna.py b/pandas/tests/copy_view/test_interp_fillna.py
index 3939fd45e1a0f..71023a538a2c3 100644
--- a/pandas/tests/copy_view/test_interp_fillna.py
+++ b/pandas/tests/copy_view/test_interp_fillna.py
@@ -113,7 +113,9 @@ def test_interpolate_cleaned_fill_method(using_copy_on_write):
     df = DataFrame({"a": ["a", np.nan, "c"], "b": 1})
     df_orig = df.copy()
 
-    result = df.interpolate(method="linear")
+    msg = "DataFrame.interpolate with object dtype"
+    with tm.assert_produces_warning(FutureWarning, match=msg):
+        result = df.interpolate(method="linear")
 
     if using_copy_on_write:
         assert np.shares_memory(get_array(result, "a"), get_array(df, "a"))
diff --git a/pandas/tests/frame/methods/test_interpolate.py b/pandas/tests/frame/methods/test_interpolate.py
index 5a3d53eb96a52..c834357d38036 100644
--- a/pandas/tests/frame/methods/test_interpolate.py
+++ b/pandas/tests/frame/methods/test_interpolate.py
@@ -69,7 +69,9 @@ def test_interp_basic(self, using_copy_on_write):
                 "D": list("abcd"),
             }
         )
-        result = df.interpolate()
+        msg = "DataFrame.interpolate with object dtype"
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            result = df.interpolate()
         tm.assert_frame_equal(result, expected)
 
         # check we didn't operate inplace GH#45791
@@ -82,7 +84,8 @@ def test_interp_basic(self, using_copy_on_write):
             assert not np.shares_memory(cvalues, result["C"]._values)
             assert not np.shares_memory(dvalues, result["D"]._values)
 
-        res = df.interpolate(inplace=True)
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            res = df.interpolate(inplace=True)
         assert res is None
         tm.assert_frame_equal(df, expected)
 
@@ -100,7 +103,9 @@ def test_interp_basic_with_non_range_index(self):
             }
         )
 
-        result = df.set_index("C").interpolate()
+        msg = "DataFrame.interpolate with object dtype"
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            result = df.set_index("C").interpolate()
         expected = df.set_index("C")
         expected.loc[3, "A"] = 3
         expected.loc[5, "B"] = 9
@@ -120,7 +125,6 @@ def test_interp_bad_method(self):
                 "A": [1, 2, np.nan, 4],
                 "B": [1, 4, 9, np.nan],
                 "C": [1, 2, 3, 5],
-                "D": list("abcd"),
             }
         )
         msg = (
diff --git a/pandas/tests/series/methods/test_interpolate.py b/pandas/tests/series/methods/test_interpolate.py
index 29f2f9f97aafe..8c4c5524ac3be 100644
--- a/pandas/tests/series/methods/test_interpolate.py
+++ b/pandas/tests/series/methods/test_interpolate.py
@@ -846,8 +846,10 @@ def test_interpolate_unsorted_index(self, ascending, expected_values):
         expected = Series(data=expected_values, index=expected_values, dtype=float)
         tm.assert_series_equal(result, expected)
 
-    def test_interpolate_afreq_raises(self):
+    def test_interpolate_asfreq_raises(self):
         ser = Series(["a", None, "b"], dtype=object)
+        msg2 = "Series.interpolate with object dtype"
         msg = "Invalid fill method"
         with pytest.raises(ValueError, match=msg):
-            ser.interpolate(method="asfreq")
+            with tm.assert_produces_warning(FutureWarning, match=msg2):
+                ser.interpolate(method="asfreq")