diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 1b12735f0e7c1..4bd31de185bb4 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -761,6 +761,7 @@ ExtensionArray
 - Bug in :meth:`.arrays.ArrowExtensionArray.__setitem__` which caused wrong behavior when using an integer array with repeated values as a key (:issue:`58530`)
 - Bug in :meth:`api.types.is_datetime64_any_dtype` where a custom :class:`ExtensionDtype` would return ``False`` for array-likes (:issue:`57055`)
 - Bug in comparison between object with :class:`ArrowDtype` and incompatible-dtyped (e.g. string vs bool) incorrectly raising instead of returning all-``False`` (for ``==``) or all-``True`` (for ``!=``) (:issue:`59505`)
+- Bug in constructing pandas data structures when passing into ``dtype`` a string of the type followed by ``[pyarrow]`` while PyArrow is not installed would raise ``NameError`` rather than ``ImportError`` (:issue:`57928`)
 - Bug in various :class:`DataFrame` reductions for pyarrow temporal dtypes returning incorrect dtype when result was null (:issue:`59234`)
 
 Styler
diff --git a/pandas/core/dtypes/dtypes.py b/pandas/core/dtypes/dtypes.py
index 96b0aa16940a6..e5d1033de4457 100644
--- a/pandas/core/dtypes/dtypes.py
+++ b/pandas/core/dtypes/dtypes.py
@@ -2344,6 +2344,8 @@ def construct_from_string(cls, string: str) -> ArrowDtype:
         if string == "string[pyarrow]":
             # Ensure Registry.find skips ArrowDtype to use StringDtype instead
             raise TypeError("string[pyarrow] should be constructed by StringDtype")
+        if pa_version_under10p1:
+            raise ImportError("pyarrow>=10.0.1 is required for ArrowDtype")
 
         base_type = string[:-9]  # get rid of "[pyarrow]"
         try:
diff --git a/pandas/tests/dtypes/test_common.py b/pandas/tests/dtypes/test_common.py
index e338fb1331734..5a59617ce5bd3 100644
--- a/pandas/tests/dtypes/test_common.py
+++ b/pandas/tests/dtypes/test_common.py
@@ -835,3 +835,10 @@ def test_pandas_dtype_string_dtypes(string_storage):
     with pd.option_context("string_storage", string_storage):
         result = pandas_dtype("string")
     assert result == pd.StringDtype(string_storage, na_value=pd.NA)
+
+
+@td.skip_if_installed("pyarrow")
+def test_construct_from_string_without_pyarrow_installed():
+    # GH 57928
+    with pytest.raises(ImportError, match="pyarrow>=10.0.1 is required"):
+        pd.Series([-1.5, 0.2, None], dtype="float32[pyarrow]")