diff --git a/doc/source/extending.rst b/doc/source/extending.rst
index 9422434a1d998..da249cb3592f4 100644
--- a/doc/source/extending.rst
+++ b/doc/source/extending.rst
@@ -160,9 +160,18 @@ your ``MyExtensionArray`` class, as follows:
     MyExtensionArray._add_arithmetic_ops()
     MyExtensionArray._add_comparison_ops()
 
-Note that since ``pandas`` automatically calls the underlying operator on each
-element one-by-one, this might not be as performant as implementing your own
-version of the associated operators directly on the ``ExtensionArray``.
+
+.. note::
+
+   Since ``pandas`` automatically calls the underlying operator on each
+   element one-by-one, this might not be as performant as implementing your own
+   version of the associated operators directly on the ``ExtensionArray``.
+
+This implementation will try to reconstruct a new ``ExtensionArray`` with the
+result of the element-wise operation. Whether or not that succeeds depends on
+whether the operation returns a result that's valid for the ``ExtensionArray``.
+If an ``ExtensionArray`` cannot be reconstructed, a list containing the scalars
+returned instead.
 
 .. _extending.extension.testing:
 
diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index 7bf13fb2fecc0..5a18a1049ee9c 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -775,10 +775,18 @@ def convert_values(param):
             res = [op(a, b) for (a, b) in zip(lvalues, rvalues)]
 
             if coerce_to_dtype:
-                try:
-                    res = self._from_sequence(res)
-                except TypeError:
-                    pass
+                if op.__name__ in {'divmod', 'rdivmod'}:
+                    try:
+                        a, b = zip(*res)
+                        res = (self._from_sequence(a),
+                               self._from_sequence(b))
+                    except TypeError:
+                        pass
+                else:
+                    try:
+                        res = self._from_sequence(res)
+                    except TypeError:
+                        pass
 
             return res
 
diff --git a/pandas/tests/extension/decimal/array.py b/pandas/tests/extension/decimal/array.py
index 387942234e6fd..f324cc2e0f345 100644
--- a/pandas/tests/extension/decimal/array.py
+++ b/pandas/tests/extension/decimal/array.py
@@ -138,5 +138,9 @@ def _concat_same_type(cls, to_concat):
         return cls(np.concatenate([x._data for x in to_concat]))
 
 
+def to_decimal(values, context=None):
+    return DecimalArray([decimal.Decimal(x) for x in values], context=context)
+
+
 DecimalArray._add_arithmetic_ops()
 DecimalArray._add_comparison_ops()
diff --git a/pandas/tests/extension/test_ops.py b/pandas/tests/extension/test_ops.py
new file mode 100644
index 0000000000000..931194b474af4
--- /dev/null
+++ b/pandas/tests/extension/test_ops.py
@@ -0,0 +1,22 @@
+import pytest
+
+from pandas.tests.extension.decimal.array import to_decimal
+import pandas.util.testing as tm
+
+
+@pytest.mark.parametrize("reverse, expected_div, expected_mod", [
+    (False, [0, 1, 1, 2], [1, 0, 1, 0]),
+    (True, [2, 1, 0, 0], [0, 0, 2, 2]),
+])
+def test_divmod(reverse, expected_div, expected_mod):
+    # https://github.com/pandas-dev/pandas/issues/22930
+    arr = to_decimal([1, 2, 3, 4])
+    if reverse:
+        div, mod = divmod(2, arr)
+    else:
+        div, mod = divmod(arr, 2)
+    expected_div = to_decimal(expected_div)
+    expected_mod = to_decimal(expected_mod)
+
+    tm.assert_extension_array_equal(div, expected_div)
+    tm.assert_extension_array_equal(mod, expected_mod)