diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 5473b7c1523f3..5dff6d729479a 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -1143,6 +1143,7 @@ ExtensionArray
 - Fixed bug where :meth:`StringArray.memory_usage` was not implemented (:issue:`33963`)
 - Fixed bug where :meth:`DataFrameGroupBy` would ignore the ``min_count`` argument for aggregations on nullable boolean dtypes (:issue:`34051`)
 - Fixed bug that `DataFrame(columns=.., dtype='string')` would fail (:issue:`27953`, :issue:`33623`)
+- Fixed bug in ``IntegerArray.astype`` to correctly copy the mask as well (:issue:`34931`).
 
 Other
 ^^^^^
diff --git a/pandas/core/arrays/integer.py b/pandas/core/arrays/integer.py
index 7be7ef3637ee5..b5cb681812939 100644
--- a/pandas/core/arrays/integer.py
+++ b/pandas/core/arrays/integer.py
@@ -448,18 +448,22 @@ def astype(self, dtype, copy: bool = True) -> ArrayLike:
             if incompatible type with an IntegerDtype, equivalent of same_kind
             casting
         """
-        from pandas.core.arrays.boolean import BooleanDtype
+        from pandas.core.arrays.masked import BaseMaskedDtype
         from pandas.core.arrays.string_ import StringDtype
 
         dtype = pandas_dtype(dtype)
 
-        # if we are astyping to an existing IntegerDtype we can fastpath
-        if isinstance(dtype, _IntegerDtype):
-            result = self._data.astype(dtype.numpy_dtype, copy=False)
-            return dtype.construct_array_type()(result, mask=self._mask, copy=False)
-        elif isinstance(dtype, BooleanDtype):
-            result = self._data.astype("bool", copy=False)
-            return dtype.construct_array_type()(result, mask=self._mask, copy=False)
+        # if the dtype is exactly the same, we can fastpath
+        if self.dtype == dtype:
+            # return the same object for copy=False
+            return self.copy() if copy else self
+        # if we are astyping to another nullable masked dtype, we can fastpath
+        if isinstance(dtype, BaseMaskedDtype):
+            data = self._data.astype(dtype.numpy_dtype, copy=copy)
+            # mask is copied depending on whether the data was copied, and
+            # not directly depending on the `copy` keyword
+            mask = self._mask if data is self._data else self._mask.copy()
+            return dtype.construct_array_type()(data, mask, copy=False)
         elif isinstance(dtype, StringDtype):
             return dtype.construct_array_type()._from_sequence(self, copy=False)
 
diff --git a/pandas/core/arrays/masked.py b/pandas/core/arrays/masked.py
index 28add129825d1..235840d6d201e 100644
--- a/pandas/core/arrays/masked.py
+++ b/pandas/core/arrays/masked.py
@@ -40,6 +40,17 @@ class BaseMaskedDtype(ExtensionDtype):
     def numpy_dtype(self) -> np.dtype:
         raise AbstractMethodError
 
+    @classmethod
+    def construct_array_type(cls) -> Type["BaseMaskedArray"]:
+        """
+        Return the array type associated with this dtype.
+
+        Returns
+        -------
+        type
+        """
+        raise NotImplementedError
+
 
 class BaseMaskedArray(ExtensionArray, ExtensionOpsMixin):
     """
diff --git a/pandas/tests/arrays/integer/test_dtypes.py b/pandas/tests/arrays/integer/test_dtypes.py
index cafe9e47a18f4..67efa4cb2ce4a 100644
--- a/pandas/tests/arrays/integer/test_dtypes.py
+++ b/pandas/tests/arrays/integer/test_dtypes.py
@@ -144,6 +144,44 @@ def test_astype(all_data):
     tm.assert_series_equal(result, expected)
 
 
+def test_astype_copy():
+    arr = pd.array([1, 2, 3, None], dtype="Int64")
+    orig = pd.array([1, 2, 3, None], dtype="Int64")
+
+    # copy=True -> ensure both data and mask are actual copies
+    result = arr.astype("Int64", copy=True)
+    assert result is not arr
+    assert not np.shares_memory(result._data, arr._data)
+    assert not np.shares_memory(result._mask, arr._mask)
+    result[0] = 10
+    tm.assert_extension_array_equal(arr, orig)
+    result[0] = pd.NA
+    tm.assert_extension_array_equal(arr, orig)
+
+    # copy=False
+    result = arr.astype("Int64", copy=False)
+    assert result is arr
+    assert np.shares_memory(result._data, arr._data)
+    assert np.shares_memory(result._mask, arr._mask)
+    result[0] = 10
+    assert arr[0] == 10
+    result[0] = pd.NA
+    assert arr[0] is pd.NA
+
+    # astype to different dtype -> always needs a copy -> even with copy=False
+    # we need to ensure that also the mask is actually copied
+    arr = pd.array([1, 2, 3, None], dtype="Int64")
+    orig = pd.array([1, 2, 3, None], dtype="Int64")
+
+    result = arr.astype("Int32", copy=False)
+    assert not np.shares_memory(result._data, arr._data)
+    assert not np.shares_memory(result._mask, arr._mask)
+    result[0] = 10
+    tm.assert_extension_array_equal(arr, orig)
+    result[0] = pd.NA
+    tm.assert_extension_array_equal(arr, orig)
+
+
 def test_astype_to_larger_numpy():
     a = pd.array([1, 2], dtype="Int32")
     result = a.astype("int64")