diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index eed48f9e46897..bccb6f991d646 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -108,7 +108,7 @@ Timezones
 
 Numeric
 ^^^^^^^
-
+- Bug in :meth:`DataFrame.quantile` with zero-column :class:`DataFrame` incorrectly raising (:issue:`23925`)
 -
 -
 
@@ -191,10 +191,6 @@ ExtensionArray
 -
 
 
-Other
-^^^^^
-
-
 .. _whatsnew_1000.contributors:
 
 Contributors
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 4beaf301988b4..46dc9204b86f5 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -8245,6 +8245,13 @@ def quantile(self, q=0.5, axis=0, numeric_only=True, interpolation="linear"):
         if is_transposed:
             data = data.T
 
+        if len(data.columns) == 0:
+            # GH#23925 _get_numeric_data may have dropped all columns
+            cols = Index([], name=self.columns.name)
+            if is_list_like(q):
+                return self._constructor([], index=q, columns=cols)
+            return self._constructor_sliced([], index=cols, name=q)
+
         result = data._data.quantile(
             qs=q, axis=1, interpolation=interpolation, transposed=is_transposed
         )
diff --git a/pandas/tests/frame/test_quantile.py b/pandas/tests/frame/test_quantile.py
index 236cadf67735d..e5e881dece34a 100644
--- a/pandas/tests/frame/test_quantile.py
+++ b/pandas/tests/frame/test_quantile.py
@@ -439,7 +439,7 @@ def test_quantile_nat(self):
         )
         tm.assert_frame_equal(res, exp)
 
-    def test_quantile_empty(self):
+    def test_quantile_empty_no_rows(self):
 
         # floats
         df = DataFrame(columns=["a", "b"], dtype="float64")
@@ -467,3 +467,17 @@ def test_quantile_empty(self):
 
         # FIXME (gives NaNs instead of NaT in 0.18.1 or 0.19.0)
         # res = df.quantile(0.5, numeric_only=False)
+
+    def test_quantile_empty_no_columns(self):
+        # GH#23925 _get_numeric_data may drop all columns
+        df = pd.DataFrame(pd.date_range("1/1/18", periods=5))
+        df.columns.name = "captain tightpants"
+        result = df.quantile(0.5)
+        expected = pd.Series([], index=[], name=0.5)
+        expected.index.name = "captain tightpants"
+        tm.assert_series_equal(result, expected)
+
+        result = df.quantile([0.5])
+        expected = pd.DataFrame([], index=[0.5], columns=[])
+        expected.columns.name = "captain tightpants"
+        tm.assert_frame_equal(result, expected)