diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 2f4e961ff433f..dabe589f86ee9 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -137,7 +137,9 @@ Other API changes
 Backwards incompatible API changes
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 - :meth:`DataFrame.swaplevels` now raises a  ``TypeError`` if the axis is not a :class:`MultiIndex`.
-  Previously a ``AttributeError`` was raised (:issue:`31126`)
+  Previously an ``AttributeError`` was raised (:issue:`31126`)
+- :meth:`DataFrame.xs` now raises a  ``TypeError`` if a ``level`` keyword is supplied and the axis is not a :class:`MultiIndex`.
+  Previously an ``AttributeError`` was raised (:issue:`33610`)
 - :meth:`DataFrameGroupby.mean` and :meth:`SeriesGroupby.mean` (and similarly for :meth:`~DataFrameGroupby.median`, :meth:`~DataFrameGroupby.std` and :meth:`~DataFrameGroupby.var`)
   now raise a  ``TypeError`` if a not-accepted keyword argument is passed into it.
   Previously a ``UnsupportedFunctionCall`` was raised (``AssertionError`` if ``min_count`` passed into :meth:`~DataFrameGroupby.median`) (:issue:`31485`)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 6a4f83427310e..c897827502eda 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -353,7 +353,7 @@ def _construct_axes_from_arguments(
         return axes, kwargs
 
     @classmethod
-    def _get_axis_number(cls, axis):
+    def _get_axis_number(cls, axis) -> int:
         axis = cls._AXIS_ALIASES.get(axis, axis)
         if is_integer(axis):
             if axis in cls._AXIS_NAMES:
@@ -366,7 +366,7 @@ def _get_axis_number(cls, axis):
         raise ValueError(f"No axis named {axis} for object type {cls.__name__}")
 
     @classmethod
-    def _get_axis_name(cls, axis):
+    def _get_axis_name(cls, axis) -> str:
         axis = cls._AXIS_ALIASES.get(axis, axis)
         if isinstance(axis, str):
             if axis in cls._AXIS_NUMBERS:
@@ -378,12 +378,12 @@ def _get_axis_name(cls, axis):
                 pass
         raise ValueError(f"No axis named {axis} for object type {cls.__name__}")
 
-    def _get_axis(self, axis):
+    def _get_axis(self, axis) -> Index:
         name = self._get_axis_name(axis)
         return getattr(self, name)
 
     @classmethod
-    def _get_block_manager_axis(cls, axis):
+    def _get_block_manager_axis(cls, axis) -> int:
         """Map the axis to the block_manager axis."""
         axis = cls._get_axis_number(axis)
         if cls._AXIS_REVERSED:
@@ -590,7 +590,9 @@ def swapaxes(self: FrameOrSeries, axis1, axis2, copy=True) -> FrameOrSeries:
         if copy:
             new_values = new_values.copy()
 
-        return self._constructor(new_values, *new_axes).__finalize__(
+        # ignore needed because of NDFrame constructor is different than
+        # DataFrame/Series constructors.
+        return self._constructor(new_values, *new_axes).__finalize__(  # type: ignore
             self, method="swapaxes"
         )
 
@@ -3490,6 +3492,8 @@ class   animal   locomotion
         axis = self._get_axis_number(axis)
         labels = self._get_axis(axis)
         if level is not None:
+            if not isinstance(labels, MultiIndex):
+                raise TypeError("Index must be a MultiIndex")
             loc, new_ax = labels.get_loc_level(key, level=level, drop_level=drop_level)
 
             # create the tuple of the indexer
@@ -7621,11 +7625,11 @@ def at_time(
         axis = self._get_axis_number(axis)
 
         index = self._get_axis(axis)
-        try:
-            indexer = index.indexer_at_time(time, asof=asof)
-        except AttributeError as err:
-            raise TypeError("Index must be DatetimeIndex") from err
 
+        if not isinstance(index, DatetimeIndex):
+            raise TypeError("Index must be DatetimeIndex")
+
+        indexer = index.indexer_at_time(time, asof=asof)
         return self._take_with_is_copy(indexer, axis=axis)
 
     def between_time(
@@ -7704,16 +7708,12 @@ def between_time(
         axis = self._get_axis_number(axis)
 
         index = self._get_axis(axis)
-        try:
-            indexer = index.indexer_between_time(
-                start_time,
-                end_time,
-                include_start=include_start,
-                include_end=include_end,
-            )
-        except AttributeError as err:
-            raise TypeError("Index must be DatetimeIndex") from err
+        if not isinstance(index, DatetimeIndex):
+            raise TypeError("Index must be DatetimeIndex")
 
+        indexer = index.indexer_between_time(
+            start_time, end_time, include_start=include_start, include_end=include_end,
+        )
         return self._take_with_is_copy(indexer, axis=axis)
 
     def resample(
diff --git a/pandas/tests/indexing/multiindex/test_xs.py b/pandas/tests/indexing/multiindex/test_xs.py
index db8c0c643a623..ff748d755c063 100644
--- a/pandas/tests/indexing/multiindex/test_xs.py
+++ b/pandas/tests/indexing/multiindex/test_xs.py
@@ -243,3 +243,15 @@ def test_series_getitem_multiindex_xs_by_label():
 
     result = s.xs("one", level="L2")
     tm.assert_series_equal(result, expected)
+
+
+def test_xs_levels_raises():
+    df = DataFrame({"A": [1, 2, 3]})
+
+    msg = "Index must be a MultiIndex"
+    with pytest.raises(TypeError, match=msg):
+        df.xs(0, level="as")
+
+    s = df.A
+    with pytest.raises(TypeError, match=msg):
+        s.xs(0, level="as")