diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 5de5bd58bd35f..2f6e97dd3db50 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -928,6 +928,17 @@ Reshaping
 Sparse
 ^^^^^^
 - Bug in :meth:`SparseArray.take` when using a different fill value than the array's fill value (:issue:`55181`)
+-
+
+ExtensionArray
+^^^^^^^^^^^^^^
+- Bug in :class:`Series` constructor giving inconsistent precision for large integer (:issue:`56566`)
+-
+
+Styler
+^^^^^^
+-
+-
 
 Other
 ^^^^^
diff --git a/pandas/core/construction.py b/pandas/core/construction.py
index d41a9c80a10ec..b3fbb75e330ae 100644
--- a/pandas/core/construction.py
+++ b/pandas/core/construction.py
@@ -47,6 +47,8 @@
     maybe_promote,
 )
 from pandas.core.dtypes.common import (
+    is_float_dtype,
+    is_integer_dtype,
     is_list_like,
     is_object_dtype,
     is_string_dtype,
@@ -503,11 +505,22 @@ 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)
+                    and len(data) > 0
+                ):
+                    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 55ca1f98f6d6c..f7724ce0a306c 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -2157,6 +2157,36 @@ 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 = Series(
+            IntegerArray(
+                np.array(
+                    [
+                        4873214862074861312,
+                        4875446630161458944,
+                        4824652147895424384,
+                        0,
+                        3526420114272476800,
+                    ],
+                    dtype="int64",
+                ),
+                np.array([0, 0, 0, 1, 0], dtype=np.bool_),
+            )
+        )
+        tm.assert_series_equal(result, expected)
+
 
 class TestSeriesConstructorIndexCoercion:
     def test_series_constructor_datetimelike_index_coercion(self):