diff --git a/pandas/core/construction.py b/pandas/core/construction.py
index f01d8822241c9..121f98b8368ca 100644
--- a/pandas/core/construction.py
+++ b/pandas/core/construction.py
@@ -36,6 +36,8 @@
 )
 from pandas.core.dtypes.common import (
     ensure_object,
+    is_float_dtype,
+    is_integer_dtype,
     is_list_like,
     is_object_dtype,
     pandas_dtype,
@@ -510,11 +512,18 @@ def sanitize_masked_array(data: ma.MaskedArray) -> np.ndarray:
     Convert numpy MaskedArray to ensure mask is softened.
     """
     mask = ma.getmaskarray(data)
+    original = data
+    original_dtype = data.dtype
     if mask.any():
         dtype, fill_value = maybe_promote(data.dtype, np.nan)
         dtype = cast(np.dtype, dtype)
         data = ma.asarray(data.astype(dtype, copy=True))
         data.soften_mask()  # set hardmask False if it was True
+        if not mask.all():
+            idx = np.unravel_index(np.nanargmax(data, axis=None), data.shape)
+            if not mask[idx] and int(data[idx]) != original[idx]:
+                if is_integer_dtype(original_dtype) and is_float_dtype(data.dtype):
+                    data = ma.asarray(original, "object")
         data[mask] = fill_value
     else:
         data = data.copy()
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 00c614cf72c20..0197dc448920f 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -2151,6 +2151,31 @@ def test_inference_on_pandas_objects(self):
             result = Series(idx)
         assert result.dtype != np.object_
 
+    def test_series_constructor_maskedarray_int_overflow(self):
+        # GH#56566
+        mx = ma.masked_array(
+            [
+                4873214862074861312,
+                4875446630161458944,
+                4824652147895424384,
+                0,
+                3526420114272476800,
+            ],
+            mask=[0, 0, 0, 1, 0],
+        )
+        result = Series(mx, dtype="Int64")
+        expected = np.array(
+            [
+                4873214862074861312,
+                4875446630161458944,
+                4824652147895424384,
+                3526420114272476800,
+            ],
+            dtype="int64",
+        )
+        result = np.array(result.dropna(ignore_index=True).values)
+        assert np.all(expected == result)
+
 
 class TestSeriesConstructorIndexCoercion:
     def test_series_constructor_datetimelike_index_coercion(self):