diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index b138e91b41661..93b63f99ea399 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -790,6 +790,7 @@ Numeric
 - Bug in :meth:`Series.__floordiv__` for :class:`ArrowDtype` with integral dtypes raising for large values (:issue:`56645`)
 - Bug in :meth:`Series.pow` not filling missing values correctly (:issue:`55512`)
 - Bug in :meth:`Series.replace` and :meth:`DataFrame.replace` matching float ``0.0`` with ``False`` and vice versa (:issue:`55398`)
+- Bug in :meth:`Series.round` raising for nullable boolean dtype (:issue:`55936`)
 
 Conversion
 ^^^^^^^^^^
diff --git a/pandas/core/arrays/masked.py b/pandas/core/arrays/masked.py
index 9ce19ced2b356..a3ff616cb8f98 100644
--- a/pandas/core/arrays/masked.py
+++ b/pandas/core/arrays/masked.py
@@ -404,6 +404,8 @@ def round(self, decimals: int = 0, *args, **kwargs):
         DataFrame.round : Round values of a DataFrame.
         Series.round : Round values of a Series.
         """
+        if self.dtype.kind == "b":
+            return self
         nv.validate_round(args, kwargs)
         values = np.round(self._data, decimals=decimals, **kwargs)
 
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 90073e21cfd66..8098d990a6a89 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -2789,13 +2789,11 @@ def round(self, decimals: int = 0, *args, **kwargs) -> Series:
         dtype: float64
         """
         nv.validate_round(args, kwargs)
-        result = self._values.round(decimals)
-        result = self._constructor(result, index=self.index, copy=False).__finalize__(
+        new_mgr = self._mgr.round(decimals=decimals, using_cow=using_copy_on_write())
+        return self._constructor_from_mgr(new_mgr, axes=new_mgr.axes).__finalize__(
             self, method="round"
         )
 
-        return result
-
     @overload
     def quantile(
         self, q: float = ..., interpolation: QuantileInterpolation = ...
diff --git a/pandas/tests/series/methods/test_round.py b/pandas/tests/series/methods/test_round.py
index 7f60c94f10e4f..c330b7a7dfbbb 100644
--- a/pandas/tests/series/methods/test_round.py
+++ b/pandas/tests/series/methods/test_round.py
@@ -63,3 +63,12 @@ def test_round_nat(self, method, freq, unit):
         round_method = getattr(ser.dt, method)
         result = round_method(freq)
         tm.assert_series_equal(result, expected)
+
+    def test_round_ea_boolean(self):
+        # GH#55936
+        ser = Series([True, False], dtype="boolean")
+        expected = ser.copy()
+        result = ser.round(2)
+        tm.assert_series_equal(result, expected)
+        result.iloc[0] = False
+        tm.assert_series_equal(ser, expected)