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..45a7d5a478bb7b 100644
--- a/pandas/core/interchange/column.py
+++ b/pandas/core/interchange/column.py
@@ -134,6 +134,7 @@ def _dtype_from_pandasdtype(self, dtype) -> tuple[DtypeKind, int, str, str]:
         # Note: 'c' (complex) not handled yet (not in array spec v1).
         #       'b', 'B' (bytes), 'S', 'a', (old-style string) 'V' (void) not handled
         #       datetime and timedelta both map to datetime (is timedelta handled?)
+        not_handled = ["b", "B", "S", "a", "V"]
 
         kind = _NP_KINDS.get(dtype.kind, None)
         if kind is None:
@@ -143,6 +144,8 @@ def _dtype_from_pandasdtype(self, dtype) -> tuple[DtypeKind, int, str, str]:
             byteorder = dtype.numpy_dtype.byteorder
         elif isinstance(dtype, DatetimeTZDtype):
             byteorder = dtype.base.byteorder  # type: ignore[union-attr]
+        elif dtype.kind in not_handled:
+            raise ValueError(f"Data type {dtype} not supported by interchange protocol")
         else:
             byteorder = dtype.byteorder