diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index a81fb584c8df9..910ef278a22a9 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -389,6 +389,7 @@ Numeric
 
 Conversion
 ^^^^^^^^^^
+- Bug in :meth:`DataFrame.astype` not casting ``values`` for Arrow-based dictionary dtype correctly (:issue:`58479`)
 - Bug in :meth:`DataFrame.update` bool dtype being converted to object (:issue:`55509`)
 - Bug in :meth:`Series.astype` might modify read-only array inplace when casting to a string dtype (:issue:`57212`)
 - Bug in :meth:`Series.reindex` not maintaining ``float32`` type when a ``reindex`` introduces a missing value (:issue:`45857`)
diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index 1154130b9bed3..0240433cdb683 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -525,6 +525,8 @@ def _box_pa_array(
         if pa_type is not None and pa_array.type != pa_type:
             if pa.types.is_dictionary(pa_type):
                 pa_array = pa_array.dictionary_encode()
+                if pa_array.type != pa_type:
+                    pa_array = pa_array.cast(pa_type)
             else:
                 try:
                     pa_array = pa_array.cast(pa_type)
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 79440b55dd5dd..7d31fe6085c3a 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -3498,6 +3498,14 @@ def test_to_numpy_timestamp_to_int():
     tm.assert_numpy_array_equal(result, expected)
 
 
+@pytest.mark.parametrize("arrow_type", [pa.large_string(), pa.string()])
+def test_cast_dictionary_different_value_dtype(arrow_type):
+    df = pd.DataFrame({"a": ["x", "y"]}, dtype="string[pyarrow]")
+    data_type = ArrowDtype(pa.dictionary(pa.int32(), arrow_type))
+    result = df.astype({"a": data_type})
+    assert result.dtypes.iloc[0] == data_type
+
+
 def test_map_numeric_na_action():
     ser = pd.Series([32, 40, None], dtype="int64[pyarrow]")
     result = ser.map(lambda x: 42, na_action="ignore")