diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 6ddb1613076acc..17a0cc31928ba2 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -280,7 +280,7 @@ Numeric
 
 Conversion
 ^^^^^^^^^^
--
+- Raise ValueError in :meth:`PandasColumn._dtype_from_pandasdtype` for currently unhandled dtypes. (:issue:`55332`)
 -
 
 Strings
diff --git a/pandas/core/interchange/column.py b/pandas/core/interchange/column.py
index acfbc5d9e6c627..6686dd86147716 100644
--- a/pandas/core/interchange/column.py
+++ b/pandas/core/interchange/column.py
@@ -144,7 +144,12 @@ def _dtype_from_pandasdtype(self, dtype) -> tuple[DtypeKind, int, str, str]:
         elif isinstance(dtype, DatetimeTZDtype):
             byteorder = dtype.base.byteorder  # type: ignore[union-attr]
         else:
-            byteorder = dtype.byteorder
+            try:
+                byteorder = dtype.byteorder
+            except AttributeError:
+                raise ValueError(
+                    f"Data type {dtype} not supported by interchange protocol"
+                )
 
         return kind, dtype.itemsize * 8, dtype_to_arrow_c_fmt(dtype), byteorder
 
diff --git a/pandas/tests/interchange/test_impl.py b/pandas/tests/interchange/test_impl.py
index 8a25a2c1889f3d..ccb710429ead8f 100644
--- a/pandas/tests/interchange/test_impl.py
+++ b/pandas/tests/interchange/test_impl.py
@@ -326,3 +326,17 @@ def test_interchange_from_non_pandas_tz_aware():
         dtype="datetime64[us, Asia/Kathmandu]",
     )
     tm.assert_frame_equal(expected, result)
+
+
+def test_not_handled() -> None:
+    pa = pytest.importorskip("pyarrow", "11.0.0")
+    df = pd.DataFrame(
+        {
+            "b": pd.Series([True, False], dtype="boolean"),
+        }
+    )
+    with pytest.raises(
+        ValueError,
+        match="Data type boolean not supported by interchange protocol",
+    ):
+        pa.interchange.from_dataframe(df)