diff --git a/doc/source/whatsnew/v0.24.0.rst b/doc/source/whatsnew/v0.24.0.rst
index 364c6f2a2daf2a..78f864f0dcb735 100644
--- a/doc/source/whatsnew/v0.24.0.rst
+++ b/doc/source/whatsnew/v0.24.0.rst
@@ -987,7 +987,8 @@ update the ``ExtensionDtype._metadata`` tuple to match the signature of your
 
 **Other changes**
 
-- ``ExtensionArray`` has gained the abstract methods ``.dropna()`` (:issue:`21185`)
+- :meth:`~pandas.api.types.ExtensionArray.dropna` has been added (:issue:`21185`)
+- :meth:`~pandas.api.types.ExtensionArray.repeat` has been added (:issue:`24349`)
 - ``ExtensionDtype`` has gained the ability to instantiate from string dtypes, e.g. ``decimal`` would instantiate a registered ``DecimalDtype``; furthermore
   the ``ExtensionDtype`` has gained the method ``construct_array_type`` (:issue:`21185`)
 - An ``ExtensionArray`` with a boolean dtype now works correctly as a boolean indexer. :meth:`pandas.api.types.is_bool_dtype` now properly considers them boolean (:issue:`22326`)
diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index cf145064fd7b17..a848dafbb06ef1 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -580,6 +580,35 @@ def factorize(self, na_sentinel=-1):
         uniques = self._from_factorized(uniques, self)
         return labels, uniques
 
+    def repeat(self, repeats, axis=None):
+        """
+        Repeat elements of an array.
+
+        .. versionadded:: 0.24.0
+
+        Parameters
+        ----------
+        repeats : int
+            This should be a non-negative integer. Repeating 0 times
+            will return an empty array.
+
+        Returns
+        -------
+        repeated_array : ExtensionArray
+            Same type as the input, with elements repeated `repeats` times.
+
+        See Also
+        --------
+        numpy.repeat : Similar method for :class:`numpy.ndarray`.
+        ExtensionArray.take : Take arbitrary positions.
+        """
+        if axis is not None:
+            raise ValueError("'axis' must be None.")
+        if repeats < 0:
+            raise ValueError("negative repeats are not allowed.")
+        ind = np.arange(len(self)).repeat(repeats)
+        return self.take(ind)
+
     # ------------------------------------------------------------------------
     # Indexing methods
     # ------------------------------------------------------------------------
diff --git a/pandas/tests/extension/base/methods.py b/pandas/tests/extension/base/methods.py
index 4a409a84f3db4a..3403d0e9e02f1b 100644
--- a/pandas/tests/extension/base/methods.py
+++ b/pandas/tests/extension/base/methods.py
@@ -264,3 +264,34 @@ def test_where_series(self, data, na_value, as_frame):
         if as_frame:
             expected = expected.to_frame(name='a')
         self.assert_equal(result, expected)
+
+    @pytest.mark.parametrize("as_series", [True, False])
+    @pytest.mark.parametrize("repeats", [0, 1, 2])
+    def test_repeat(self, data, repeats, as_series):
+        a, b, c = data[:3]
+        arr = type(data)._from_sequence([a, b, c], dtype=data.dtype)
+
+        if as_series:
+            arr = pd.Series(arr)
+
+        result = arr.repeat(repeats)
+
+        if repeats == 0:
+            expected = []
+        elif repeats == 1:
+            expected = [a, b, c]
+        else:
+            expected = [a, a, b, b, c, c]
+        expected = type(data)._from_sequence(expected, dtype=data.dtype)
+        if as_series:
+            index = pd.Series(np.arange(len(arr))).repeat(repeats).index
+            expected = pd.Series(expected, index=index)
+        self.assert_equal(result, expected)
+
+    def test_repeat_raises(self, data):
+        with pytest.raises(ValueError, match="'axis'"):
+            data.repeat(2, axis=1)
+
+        with pytest.raises(ValueError,
+                           match="negative"):
+            data.repeat(-1)