diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index d2f88b353e1c1..4e83284cb96ed 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -1643,7 +1643,7 @@ def fillna(self, value=None, method=None, limit=None):
 
             # TODO: dispatch when self.categories is EA-dtype
             values = np.asarray(self).reshape(-1, len(self))
-            values = interpolate_2d(values, method, 0, None, value).astype(
+            values = interpolate_2d(values, method, 0, None).astype(
                 self.categories.dtype
             )[0]
             codes = _get_codes_for_values(values, self.categories)
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index f18bc4d0bcf85..278d71068b7bf 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1181,12 +1181,15 @@ def interpolate(
             m = None
 
         if m is not None:
+            if fill_value is not None:
+                # similar to validate_fillna_kwargs
+                raise ValueError("Cannot pass both fill_value and method")
+
             return self._interpolate_with_fill(
                 method=m,
                 axis=axis,
                 inplace=inplace,
                 limit=limit,
-                fill_value=fill_value,
                 coerce=coerce,
                 downcast=downcast,
             )
@@ -1214,7 +1217,6 @@ def _interpolate_with_fill(
         axis: int = 0,
         inplace: bool = False,
         limit: Optional[int] = None,
-        fill_value: Optional[Any] = None,
         coerce: bool = False,
         downcast: Optional[str] = None,
     ) -> List["Block"]:
@@ -1232,16 +1234,11 @@ def _interpolate_with_fill(
 
         values = self.values if inplace else self.values.copy()
 
-        # We only get here for non-ExtensionBlock
-        fill_value = convert_scalar_for_putitemlike(fill_value, self.values.dtype)
-
         values = missing.interpolate_2d(
             values,
             method=method,
             axis=axis,
             limit=limit,
-            fill_value=fill_value,
-            dtype=self.dtype,
         )
 
         blocks = [self.make_block_same_class(values, ndim=self.ndim)]
diff --git a/pandas/core/missing.py b/pandas/core/missing.py
index edcdf2f54bc4c..f4182027e9e04 100644
--- a/pandas/core/missing.py
+++ b/pandas/core/missing.py
@@ -545,8 +545,6 @@ def interpolate_2d(
     method="pad",
     axis=0,
     limit=None,
-    fill_value=None,
-    dtype: Optional[DtypeObj] = None,
 ):
     """
     Perform an actual interpolation of values, values will be make 2-d if
@@ -563,18 +561,11 @@ def interpolate_2d(
             raise AssertionError("cannot interpolate on a ndim == 1 with axis != 0")
         values = values.reshape(tuple((1,) + values.shape))
 
-    if fill_value is None:
-        mask = None
-    else:  # todo create faster fill func without masking
-        mask = mask_missing(transf(values), fill_value)
-
     method = clean_fill_method(method)
     if method == "pad":
-        values = transf(pad_2d(transf(values), limit=limit, mask=mask, dtype=dtype))
+        values = transf(pad_2d(transf(values), limit=limit))
     else:
-        values = transf(
-            backfill_2d(transf(values), limit=limit, mask=mask, dtype=dtype)
-        )
+        values = transf(backfill_2d(transf(values), limit=limit))
 
     # reshape back
     if ndim == 1:
diff --git a/pandas/tests/series/methods/test_interpolate.py b/pandas/tests/series/methods/test_interpolate.py
index cba9443005f2f..9fc468221ee2d 100644
--- a/pandas/tests/series/methods/test_interpolate.py
+++ b/pandas/tests/series/methods/test_interpolate.py
@@ -340,6 +340,14 @@ def test_interp_invalid_method(self, invalid_method):
         with pytest.raises(ValueError, match=msg):
             s.interpolate(method=invalid_method, limit=-1)
 
+    def test_interp_invalid_method_and_value(self):
+        # GH#36624
+        ser = Series([1, 3, np.nan, 12, np.nan, 25])
+
+        msg = "Cannot pass both fill_value and method"
+        with pytest.raises(ValueError, match=msg):
+            ser.interpolate(fill_value=3, method="pad")
+
     def test_interp_limit_forward(self):
         s = Series([1, 3, np.nan, np.nan, np.nan, 11])