diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index ba5334b2f4fa8..e5dd9e6eb86cc 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -406,6 +406,7 @@ Missing
 ^^^^^^^
 - Bug in :meth:`DataFrame.interpolate` ignoring ``inplace`` when :class:`DataFrame` is empty (:issue:`53199`)
 - Bug in :meth:`Series.interpolate` and :meth:`DataFrame.interpolate` failing to raise on invalid ``downcast`` keyword, which can be only ``None`` or "infer" (:issue:`53103`)
+- Bug in :meth:`Series.interpolate` and :meth:`DataFrame.interpolate` with complex dtype incorrectly failing to fill ``NaN`` entries (:issue:`53635`)
 -
 
 MultiIndex
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index d0efa402089dc..981e29df2c323 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1375,7 +1375,7 @@ def interpolate(
             if method == "asfreq":  # type: ignore[comparison-overlap]
                 # clean_fill_method used to allow this
                 raise
-        if m is None and self.dtype.kind != "f":
+        if m is None and self.dtype == _dtype_obj:
             # only deal with floats
             # bc we already checked that can_hold_na, we don't have int dtype here
             # test_interp_basic checks that we make a copy here
diff --git a/pandas/tests/frame/methods/test_interpolate.py b/pandas/tests/frame/methods/test_interpolate.py
index 5a3d53eb96a52..151e281b5ded2 100644
--- a/pandas/tests/frame/methods/test_interpolate.py
+++ b/pandas/tests/frame/methods/test_interpolate.py
@@ -13,6 +13,20 @@
 
 
 class TestDataFrameInterpolate:
+    def test_interpolate_complex(self):
+        # GH#53635
+        ser = Series([complex("1+1j"), float("nan"), complex("2+2j")])
+        assert ser.dtype.kind == "c"
+
+        res = ser.interpolate()
+        expected = Series([ser[0], ser[0] * 1.5, ser[2]])
+        tm.assert_series_equal(res, expected)
+
+        df = ser.to_frame()
+        res = df.interpolate()
+        expected = expected.to_frame()
+        tm.assert_frame_equal(res, expected)
+
     def test_interpolate_datetimelike_values(self, frame_or_series):
         # GH#11312, GH#51005
         orig = Series(date_range("2012-01-01", periods=5))