diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 7fddb36185789..5d1668514c0a6 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -482,6 +482,7 @@ Other
 - Bug in :class:`DataFrame` when passing a ``dict`` with a NA scalar and ``columns`` that would always return ``np.nan`` (:issue:`57205`)
 - Bug in :func:`eval` where the names of the :class:`Series` were not preserved when using ``engine="numexpr"``. (:issue:`10239`)
 - Bug in :func:`unique` on :class:`Index` not always returning :class:`Index` (:issue:`57043`)
+- Bug in :func:`mask` to handle NaN values in condition of function. (:issue:`56844`)
 - Bug in :meth:`DataFrame.eval` and :meth:`DataFrame.query` which caused an exception when using NumPy attributes via ``@`` notation, e.g., ``df.eval("@np.floor(a)")``. (:issue:`58041`)
 - Bug in :meth:`DataFrame.eval` and :meth:`DataFrame.query` which did not allow to use ``tan`` function. (:issue:`55091`)
 - Bug in :meth:`DataFrame.sort_index` when passing ``axis="columns"`` and ``ignore_index=True`` and ``ascending=False`` not returning a :class:`RangeIndex` columns (:issue:`57293`)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 3da047eaa2d4e..a61b42712e999 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -9999,6 +9999,9 @@ def mask(
         cond = common.apply_if_callable(cond, self)
         other = common.apply_if_callable(other, self)
 
+        if isinstance(cond, (ABCDataFrame, ABCSeries)):
+            cond = cond.fillna(False)
+
         # see gh-21891
         if not hasattr(cond, "__invert__"):
             cond = np.array(cond)
diff --git a/pandas/tests/frame/indexing/test_mask.py b/pandas/tests/frame/indexing/test_mask.py
index 264e27c9c122e..014f038158033 100644
--- a/pandas/tests/frame/indexing/test_mask.py
+++ b/pandas/tests/frame/indexing/test_mask.py
@@ -150,3 +150,12 @@ def test_mask_inplace_no_other():
     df.mask(cond, inplace=True)
     expected = DataFrame({"a": [np.nan, 2], "b": ["x", np.nan]})
     tm.assert_frame_equal(df, expected)
+
+
+def test_mask_with_NA():
+    df = DataFrame({"A": [0, 1, 2]})
+    cond = Series([True, False, pd.NA], dtype=pd.BooleanDtype())
+
+    result = df.mask(cond, other=100)
+    expected = DataFrame({"A": [100, 1, 2]})
+    tm.assert_frame_equal(result, expected)