diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index c865509dea172..35f66f7aebd17 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -742,6 +742,7 @@ Other Deprecations
 - Deprecated silent casting of non-datetime 'other' to datetime in :meth:`Series.combine_first` (:issue:`62931`)
 - Deprecated slicing on a :class:`Series` or :class:`DataFrame` with a :class:`DatetimeIndex` using a ``datetime.date`` object, explicitly cast to :class:`Timestamp` instead (:issue:`35830`)
 - Deprecated support for the Dataframe Interchange Protocol (:issue:`56732`)
+- Deprecated the "columns" keyword in :meth:`Series.drop` as it was silently ignored (:issue:`39509`)
 - Deprecated the 'inplace' keyword from :meth:`Resampler.interpolate`, as passing ``True`` raises ``AttributeError`` (:issue:`58690`)
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 1a8645cf1815d..5bcba0b1b09b8 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -53,6 +53,7 @@
 from pandas.util._decorators import (
     Appender,
     Substitution,
+    deprecate_kwarg,
     deprecate_nonkeyword_arguments,
     doc,
     set_module,
@@ -5509,6 +5510,7 @@ def drop(
         errors: IgnoreRaise = ...,
     ) -> Series | None: ...
 
+    @deprecate_kwarg(Pandas4Warning, "columns", new_arg_name=None)  # GH#39509
     def drop(
         self,
         labels: IndexLabel | ListLike = None,
@@ -5537,7 +5539,9 @@ def drop(
             Redundant for application on Series, but 'index' can be used instead
             of 'labels'.
         columns : single label or list-like
-            No change is made to the Series; use 'index' or 'labels' instead.
+            Not supported; use 'index' or 'labels' instead.
+
+            .. deprecated:: 3.0.0
         level : int or level name, optional
             For MultiIndex, level for which the labels will be removed.
         inplace : bool, default False
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index e6f84941f6b1a..61483879d0552 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -680,7 +680,8 @@ def __init__(
         # GH 32262: It's convention to keep the grouping column in
         # groupby.<agg_func>, but unexpected to users in
         # groupby.rolling.<agg_func>
-        obj = obj.drop(columns=self._grouper.names, errors="ignore")
+        if obj.ndim == 2:
+            obj = obj.drop(columns=self._grouper.names, errors="ignore")
         # GH 15354
         if kwargs.get("step") is not None:
             raise NotImplementedError("step not implemented for groupby")
@@ -715,7 +716,7 @@ def _apply(
             if key not in self.obj.index.names or key is None
         ]
 
-        if len(drop_columns) != len(groupby_keys):
+        if len(drop_columns) != len(groupby_keys) and result.ndim == 2:
             # Our result will have still kept the column in the result
             result = result.drop(columns=drop_columns, errors="ignore")
 
@@ -758,8 +759,9 @@ def _apply_pairwise(
         """
         Apply the given pairwise function given 2 pandas objects (DataFrame/Series)
         """
-        # Manually drop the grouping column first
-        target = target.drop(columns=self._grouper.names, errors="ignore")
+        if target.ndim == 2:
+            # Manually drop the grouping column first
+            target = target.drop(columns=self._grouper.names, errors="ignore")
         result = super()._apply_pairwise(target, other, pairwise, func, numeric_only)
         # 1) Determine the levels + codes of the groupby levels
         if other is not None and not all(
diff --git a/pandas/tests/series/methods/test_drop.py b/pandas/tests/series/methods/test_drop.py
index d2a5a3324e886..5ed5dbe066c73 100644
--- a/pandas/tests/series/methods/test_drop.py
+++ b/pandas/tests/series/methods/test_drop.py
@@ -1,5 +1,7 @@
 import pytest
 
+from pandas.errors import Pandas4Warning
+
 from pandas import (
     Index,
     Series,
@@ -97,3 +99,12 @@ def test_drop_index_ea_dtype(any_numeric_ea_dtype):
     result = df.drop(idx)
     expected = Series(100, index=Index([1], dtype=any_numeric_ea_dtype))
     tm.assert_series_equal(result, expected)
+
+
+def test_drop_series_columns_deprecated():
+    # GH#39509
+    ser = Series({"a": 1, "b": 3})
+
+    msg = "the 'columns' keyword is deprecated and will be removed"
+    with tm.assert_produces_warning(Pandas4Warning, match=msg):
+        ser.drop(columns=["a"])