diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 63902b53ea36d..155486953f4ba 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -570,6 +570,7 @@ Conversion
 - Bug in creating a :class:`DataFrame` from an empty ``np.recarray`` not retaining the original dtypes (:issue:`40121`)
 - Bug in :class:`DataFrame` failing to raise ``TypeError`` when constructing from a ``frozenset`` (:issue:`40163`)
 - Bug in :class:`Index` construction silently ignoring a passed ``dtype`` when the data cannot be cast to that dtype (:issue:`21311`)
+- Bug in :meth:`StringArray.astype` falling back to numpy and raising when converting to ``dtype='categorical'`` (:issue:`40450`)
 - Bug in :class:`DataFrame` construction with a dictionary containing an arraylike with ``ExtensionDtype`` and ``copy=True`` failing to make a copy (:issue:`38939`)
 -
 
diff --git a/pandas/core/arrays/string_.py b/pandas/core/arrays/string_.py
index 0a2893ac49a49..666afb65e19ff 100644
--- a/pandas/core/arrays/string_.py
+++ b/pandas/core/arrays/string_.py
@@ -327,6 +327,9 @@ def astype(self, dtype, copy=True):
             arr[mask] = "0"
             values = arr.astype(dtype.numpy_dtype)
             return FloatingArray(values, mask, copy=False)
+        elif isinstance(dtype, ExtensionDtype):
+            cls = dtype.construct_array_type()
+            return cls._from_sequence(self, dtype=dtype, copy=copy)
         elif np.issubdtype(dtype, np.floating):
             arr = self._ndarray.copy()
             mask = self.isna()
diff --git a/pandas/tests/series/methods/test_astype.py b/pandas/tests/series/methods/test_astype.py
index 4e068690c41e5..d23c44733949a 100644
--- a/pandas/tests/series/methods/test_astype.py
+++ b/pandas/tests/series/methods/test_astype.py
@@ -350,6 +350,38 @@ def test_astype_bytes(self):
         assert result.dtypes == np.dtype("S3")
 
 
+class TestAstypeString:
+    @pytest.mark.parametrize(
+        "data, dtype",
+        [
+            ([True, NA], "boolean"),
+            (["A", NA], "category"),
+            (["2020-10-10", "2020-10-10"], "datetime64[ns]"),
+            (["2020-10-10", "2020-10-10", NaT], "datetime64[ns]"),
+            (
+                ["2012-01-01 00:00:00-05:00", NaT],
+                "datetime64[ns, US/Eastern]",
+            ),
+            ([1, None], "UInt16"),
+            (["1/1/2021", "2/1/2021"], "period[M]"),
+            (["1/1/2021", "2/1/2021", NaT], "period[M]"),
+            (["1 Day", "59 Days", NaT], "timedelta64[ns]"),
+            # currently no way to parse IntervalArray from a list of strings
+        ],
+    )
+    def test_astype_string_to_extension_dtype_roundtrip(self, data, dtype, request):
+        if dtype == "boolean" or (
+            dtype in ("period[M]", "datetime64[ns]", "timedelta64[ns]") and NaT in data
+        ):
+            mark = pytest.mark.xfail(
+                reason="TODO StringArray.astype() with missing values #GH40566"
+            )
+            request.node.add_marker(mark)
+        # GH-40351
+        s = Series(data, dtype=dtype)
+        tm.assert_series_equal(s, s.astype("string").astype(dtype))
+
+
 class TestAstypeCategorical:
     def test_astype_categorical_to_other(self):
         cat = Categorical([f"{i} - {i + 499}" for i in range(0, 10000, 500)])