diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index ffa65032e6aae..c098a3b2443c4 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -951,6 +951,7 @@ Missing
 ^^^^^^^
 - Bug in :meth:`DataFrame.fillna` and :meth:`Series.fillna` that would ignore the ``limit`` argument on :class:`.ExtensionArray` dtypes (:issue:`58001`)
 - Bug in :meth:`NA.__and__`, :meth:`NA.__or__` and :meth:`NA.__xor__` when operating with ``np.bool_`` objects (:issue:`58427`)
+- Bug in ``divmod`` between :class:`NA` and ``Int64`` dtype objects (:issue:`62196`)
 -
 
 MultiIndex
diff --git a/pandas/core/arrays/masked.py b/pandas/core/arrays/masked.py
index ce7f288fc0238..b00e362e1309a 100644
--- a/pandas/core/arrays/masked.py
+++ b/pandas/core/arrays/masked.py
@@ -791,6 +791,10 @@ def _arith_method(self, other, op):
                 #  will be all-True, but since this is division, we want
                 #  to end up with floating dtype.
                 result = result.astype(np.float64)
+            elif op_name in {"divmod", "rdivmod"}:
+                # GH#62196
+                res = self._maybe_mask_result(result, mask)
+                return res, res.copy()
         else:
             # Make sure we do this before the "pow" mask checks
             #  to get an expected exception message on shape mismatch.
diff --git a/pandas/tests/arrays/masked/test_arithmetic.py b/pandas/tests/arrays/masked/test_arithmetic.py
index ea018d2da4d26..779531d525505 100644
--- a/pandas/tests/arrays/masked/test_arithmetic.py
+++ b/pandas/tests/arrays/masked/test_arithmetic.py
@@ -246,3 +246,26 @@ def test_unary_op_does_not_propagate_mask(data, op):
     expected = result.copy(deep=True)
     ser[0] = None
     tm.assert_series_equal(result, expected)
+
+
+@pytest.mark.parametrize("dtype", ["Int64", "Int32", "Float32", "Float64"])
+def test_divmod_pdna(dtype):
+    # GH#62196
+    ser = pd.Series([1, 2, 3], dtype=dtype)
+    res = divmod(pd.NA, ser)
+    assert isinstance(res, tuple) and len(res) == 2
+
+    exp = pd.Series([pd.NA, pd.NA, pd.NA], dtype=dtype)
+    tm.assert_series_equal(res[0], exp)
+    tm.assert_series_equal(res[1], exp)
+
+    tm.assert_series_equal(res[0], pd.NA // ser)
+    tm.assert_series_equal(res[1], pd.NA % ser)
+
+    res = divmod(ser, pd.NA)
+    assert isinstance(res, tuple) and len(res) == 2
+    tm.assert_series_equal(res[0], exp)
+    tm.assert_series_equal(res[1], exp)
+
+    tm.assert_series_equal(res[0], ser // pd.NA)
+    tm.assert_series_equal(res[1], ser % pd.NA)