diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 4605c14643fa2..a3499f857d158 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -339,6 +339,8 @@ Backwards incompatible API changes
 - Combining a ``Categorical`` with integer categories and which contains missing values
   with a float dtype column in operations such as :func:`concat` or :meth:`~DataFrame.append`
   will now result in a float column instead of an object dtyped column (:issue:`33607`)
+- :meth:`Series.to_timestamp` now raises a ``TypeError`` if the axis is not a :class:`PeriodIndex`. Previously an ``AttributeError`` was raised (:issue:`33327`)
+- :meth:`Series.to_period` now raises a ``TypeError`` if the axis is not a :class:`DatetimeIndex`. Previously an ``AttributeError`` was raised (:issue:`33327`)
 
 ``MultiIndex.get_indexer`` interprets `method` argument differently
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 4ba9a0c925a5d..e107b66d33b1c 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -4684,7 +4684,8 @@ def to_timestamp(self, freq=None, how="start", copy=True) -> "Series":
         if copy:
             new_values = new_values.copy()
 
-        assert isinstance(self.index, PeriodIndex)
+        if not isinstance(self.index, PeriodIndex):
+            raise TypeError(f"unsupported Type {type(self.index).__name__}")
         new_index = self.index.to_timestamp(freq=freq, how=how)  # type: ignore
         return self._constructor(new_values, index=new_index).__finalize__(
             self, method="to_timestamp"
@@ -4711,7 +4712,8 @@ def to_period(self, freq=None, copy=True) -> "Series":
         if copy:
             new_values = new_values.copy()
 
-        assert isinstance(self.index, DatetimeIndex)
+        if not isinstance(self.index, DatetimeIndex):
+            raise TypeError(f"unsupported Type {type(self.index).__name__}")
         new_index = self.index.to_period(freq=freq)  # type: ignore
         return self._constructor(new_values, index=new_index).__finalize__(
             self, method="to_period"
diff --git a/pandas/tests/series/methods/test_to_period.py b/pandas/tests/series/methods/test_to_period.py
index 28c4aad3edf32..5bc4a36498c58 100644
--- a/pandas/tests/series/methods/test_to_period.py
+++ b/pandas/tests/series/methods/test_to_period.py
@@ -1,4 +1,5 @@
 import numpy as np
+import pytest
 
 from pandas import (
     DataFrame,
@@ -45,3 +46,12 @@ def test_to_period(self):
         expected = df.copy()
         expected.columns = exp_idx
         tm.assert_frame_equal(df.to_period(axis=1), expected)
+
+    def test_to_period_raises(self, indices):
+        # https://github.com/pandas-dev/pandas/issues/33327
+        index = indices
+        ser = Series(index=index, dtype=object)
+        if not isinstance(index, DatetimeIndex):
+            msg = f"unsupported Type {type(index).__name__}"
+            with pytest.raises(TypeError, match=msg):
+                ser.to_period()
diff --git a/pandas/tests/series/methods/test_to_timestamp.py b/pandas/tests/series/methods/test_to_timestamp.py
index 44caf1f082a4f..296a1c15619f2 100644
--- a/pandas/tests/series/methods/test_to_timestamp.py
+++ b/pandas/tests/series/methods/test_to_timestamp.py
@@ -1,6 +1,8 @@
 from datetime import timedelta
 
-from pandas import Series, Timedelta, date_range, period_range, to_datetime
+import pytest
+
+from pandas import PeriodIndex, Series, Timedelta, date_range, period_range, to_datetime
 import pandas._testing as tm
 
 
@@ -52,3 +54,12 @@ def _get_with_delta(delta, freq="A-DEC"):
         exp_index = exp_index + Timedelta(1, "s") - Timedelta(1, "ns")
         tm.assert_index_equal(result.index, exp_index)
         assert result.name == "foo"
+
+    def test_to_timestamp_raises(self, indices):
+        # https://github.com/pandas-dev/pandas/issues/33327
+        index = indices
+        ser = Series(index=index, dtype=object)
+        if not isinstance(index, PeriodIndex):
+            msg = f"unsupported Type {type(index).__name__}"
+            with pytest.raises(TypeError, match=msg):
+                ser.to_timestamp()