diff --git a/doc/source/whatsnew/v1.0.1.rst b/doc/source/whatsnew/v1.0.1.rst
index e0182e4e3c1f2..f41eca9d6b846 100644
--- a/doc/source/whatsnew/v1.0.1.rst
+++ b/doc/source/whatsnew/v1.0.1.rst
@@ -56,6 +56,9 @@ Bug fixes
 
 - Plotting tz-aware timeseries no longer gives UserWarning (:issue:`31205`)
 
+**Interval**
+
+- Bug in :meth:`Series.shift` with ``interval`` dtype raising a ``TypeError`` when shifting an interval array of integers or datetimes (:issue:`34195`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/arrays/interval.py b/pandas/core/arrays/interval.py
index 23cf5f317ac7d..cc41ac1dc19a9 100644
--- a/pandas/core/arrays/interval.py
+++ b/pandas/core/arrays/interval.py
@@ -27,6 +27,7 @@
 from pandas.core.dtypes.dtypes import IntervalDtype
 from pandas.core.dtypes.generic import (
     ABCDatetimeIndex,
+    ABCExtensionArray,
     ABCIndexClass,
     ABCInterval,
     ABCIntervalIndex,
@@ -789,6 +790,33 @@ def size(self) -> int:
         # Avoid materializing self.values
         return self.left.size
 
+    def shift(self, periods: int = 1, fill_value: object = None) -> ABCExtensionArray:
+        if not len(self) or periods == 0:
+            return self.copy()
+
+        if isna(fill_value):
+            fill_value = self.dtype.na_value
+
+        # ExtensionArray.shift doesn't work for two reasons
+        # 1. IntervalArray.dtype.na_value may not be correct for the dtype.
+        # 2. IntervalArray._from_sequence only accepts NaN for missing values,
+        #    not other values like NaT
+
+        empty_len = min(abs(periods), len(self))
+        if isna(fill_value):
+            fill_value = self.left._na_value
+            empty = IntervalArray.from_breaks([fill_value] * (empty_len + 1))
+        else:
+            empty = self._from_sequence([fill_value] * empty_len)
+
+        if periods > 0:
+            a = empty
+            b = self[:-periods]
+        else:
+            a = self[abs(periods) :]
+            b = empty
+        return self._concat_same_type([a, b])
+
     def take(self, indices, allow_fill=False, fill_value=None, axis=None, **kwargs):
         """
         Take elements from the IntervalArray.
diff --git a/pandas/tests/arrays/interval/test_interval.py b/pandas/tests/arrays/interval/test_interval.py
index e046d87780bb4..a43ea7e40a16a 100644
--- a/pandas/tests/arrays/interval/test_interval.py
+++ b/pandas/tests/arrays/interval/test_interval.py
@@ -81,6 +81,24 @@ def test_where_raises(self, other):
         with pytest.raises(ValueError, match=match):
             ser.where([True, False, True], other=other)
 
+    def test_shift(self):
+        # https://github.com/pandas-dev/pandas/issues/31495
+        a = IntervalArray.from_breaks([1, 2, 3])
+        result = a.shift()
+        # int -> float
+        expected = IntervalArray.from_tuples([(np.nan, np.nan), (1.0, 2.0)])
+        tm.assert_interval_array_equal(result, expected)
+
+    def test_shift_datetime(self):
+        a = IntervalArray.from_breaks(pd.date_range("2000", periods=4))
+        result = a.shift(2)
+        expected = a.take([-1, -1, 0], allow_fill=True)
+        tm.assert_interval_array_equal(result, expected)
+
+        result = a.shift(-1)
+        expected = a.take([1, 2, -1], allow_fill=True)
+        tm.assert_interval_array_equal(result, expected)
+
 
 class TestSetitem:
     def test_set_na(self, left_right_dtypes):
diff --git a/pandas/tests/extension/base/methods.py b/pandas/tests/extension/base/methods.py
index 24ab7fe3fc845..6ed8b782deffa 100644
--- a/pandas/tests/extension/base/methods.py
+++ b/pandas/tests/extension/base/methods.py
@@ -280,6 +280,13 @@ def test_shift_empty_array(self, data, periods):
         expected = empty
         self.assert_extension_array_equal(result, expected)
 
+    def test_shift_zero_copies(self, data):
+        result = data.shift(0)
+        assert result is not data
+
+        result = data[:0].shift(2)
+        assert result is not data
+
     def test_shift_fill_value(self, data):
         arr = data[:4]
         fill_value = data[0]