diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 25e482fea60eee..1eb22436204a8e 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -648,6 +648,7 @@ Deprecations
 - Deprecated setting :attr:`Categorical._codes`, create a new :class:`Categorical` with the desired codes instead (:issue:`40606`)
 - Deprecated behavior of :meth:`DatetimeIndex.union` with mixed timezones; in a future version both will be cast to UTC instead of object dtype (:issue:`39328`)
 - Deprecated using ``usecols`` with out of bounds indices for ``read_csv`` with ``engine="c"`` (:issue:`25623`)
+- Deprecated passing arguments as positional (except for ``"method"``) in :meth:`DataFrame.interpolate` and :meth:`Series.interpolate` (:issue:`41485`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 1fa149cd834b0e..6aa537d37aea2f 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -77,6 +77,7 @@
     Appender,
     Substitution,
     deprecate_kwarg,
+    deprecate_nonkeyword_arguments,
     doc,
     rewrite_axis_style_signature,
 )
@@ -10632,6 +10633,29 @@ def values(self) -> np.ndarray:
         self._consolidate_inplace()
         return self._mgr.as_array(transpose=True)
 
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self", "method"])
+    def interpolate(
+        self: DataFrame,
+        method: str = "linear",
+        axis: Axis = 0,
+        limit: int | None = None,
+        inplace: bool = False,
+        limit_direction: str | None = None,
+        limit_area: str | None = None,
+        downcast: str | None = None,
+        **kwargs,
+    ) -> DataFrame | None:
+        return super().interpolate(
+            method,
+            axis,
+            limit,
+            inplace,
+            limit_direction,
+            limit_area,
+            downcast,
+            **kwargs,
+        )
+
 
 DataFrame._add_numeric_operations()
 
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index a09cc0a6324c00..3c69ba4e6bdf0f 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -6696,7 +6696,6 @@ def replace(
         else:
             return result.__finalize__(self, method="replace")
 
-    @final
     def interpolate(
         self: FrameOrSeries,
         method: str = "linear",
diff --git a/pandas/core/series.py b/pandas/core/series.py
index d0ff50cca53550..aaf37ad191e876 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -51,6 +51,7 @@
 from pandas.util._decorators import (
     Appender,
     Substitution,
+    deprecate_nonkeyword_arguments,
     doc,
 )
 from pandas.util._validators import (
@@ -5256,6 +5257,29 @@ def to_period(self, freq=None, copy=True) -> Series:
             self, method="to_period"
         )
 
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self", "method"])
+    def interpolate(
+        self: Series,
+        method: str = "linear",
+        axis: Axis = 0,
+        limit: int | None = None,
+        inplace: bool = False,
+        limit_direction: str | None = None,
+        limit_area: str | None = None,
+        downcast: str | None = None,
+        **kwargs,
+    ) -> Series | None:
+        return super().interpolate(
+            method,
+            axis,
+            limit,
+            inplace,
+            limit_direction,
+            limit_area,
+            downcast,
+            **kwargs,
+        )
+
     # ----------------------------------------------------------------------
     # Add index
     _AXIS_ORDERS = ["index"]
diff --git a/pandas/tests/frame/methods/test_interpolate.py b/pandas/tests/frame/methods/test_interpolate.py
index 5c6fcec887dfb9..d0551ffd5cffe3 100644
--- a/pandas/tests/frame/methods/test_interpolate.py
+++ b/pandas/tests/frame/methods/test_interpolate.py
@@ -342,3 +342,15 @@ def test_interp_fillna_methods(self, axis, method):
         expected = df.fillna(axis=axis, method=method)
         result = df.interpolate(method=method, axis=axis)
         tm.assert_frame_equal(result, expected)
+
+    def test_interpolate_pos_args_deprecation(self):
+        # https://github.com/pandas-dev/pandas/issues/41485
+        df = DataFrame({"a": [1, 2, 3]})
+        msg = (
+            r"In a future version of pandas all arguments of DataFrame.interpolate "
+            r"except for the argument 'method' will be keyword-only"
+        )
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            result = df.interpolate("pad", 0)
+        expected = DataFrame({"a": [1, 2, 3]})
+        tm.assert_frame_equal(result, expected)
diff --git a/pandas/tests/series/methods/test_interpolate.py b/pandas/tests/series/methods/test_interpolate.py
index 5686e6478772df..8ca2d37016691d 100644
--- a/pandas/tests/series/methods/test_interpolate.py
+++ b/pandas/tests/series/methods/test_interpolate.py
@@ -811,3 +811,15 @@ def test_interpolate_unsorted_index(self, ascending, expected_values):
         result = ts.sort_index(ascending=ascending).interpolate(method="index")
         expected = Series(data=expected_values, index=expected_values, dtype=float)
         tm.assert_series_equal(result, expected)
+
+    def test_interpolate_pos_args_deprecation(self):
+        # https://github.com/pandas-dev/pandas/issues/41485
+        ser = Series([1, 2, 3])
+        msg = (
+            r"In a future version of pandas all arguments of Series.interpolate except "
+            r"for the argument 'method' will be keyword-only"
+        )
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            result = ser.interpolate("pad", 0)
+        expected = Series([1, 2, 3])
+        tm.assert_series_equal(result, expected)