diff --git a/CHANGES b/CHANGES
index 8243e3471..6a7735552 100644
--- a/CHANGES
+++ b/CHANGES
@@ -24,6 +24,8 @@ Pint Changelog
   (PR #1949)
 - Fix unhandled TypeError when auto_reduce_dimensions=True and non_int_type=Decimal
   (PR #1853)
+- Creating prefixed offset units now raises an error.
+  (PR #1998)
 - Improved error message in `get_dimensionality()` when non existent units are passed.
   (PR #1874, Issue #1716)
 
diff --git a/pint/facets/plain/registry.py b/pint/facets/plain/registry.py
index 09fd220ee..b459635f9 100644
--- a/pint/facets/plain/registry.py
+++ b/pint/facets/plain/registry.py
@@ -60,7 +60,12 @@
     UnitLike,
 )
 from ...compat import Self, TypeAlias, deprecated
-from ...errors import DimensionalityError, RedefinitionError, UndefinedUnitError
+from ...errors import (
+    DimensionalityError,
+    OffsetUnitCalculusError,
+    RedefinitionError,
+    UndefinedUnitError,
+)
 from ...pint_eval import build_eval_tree
 from ...util import (
     ParserHelper,
@@ -664,6 +669,11 @@ def get_name(self, name_or_alias: str, case_sensitive: bool | None = None) -> st
             )
 
         if prefix:
+            if not self._units[unit_name].is_multiplicative:
+                raise OffsetUnitCalculusError(
+                    "Prefixing a unit requires multiplying the unit."
+                )
+
             name = prefix + unit_name
             symbol = self.get_symbol(name, case_sensitive)
             prefix_def = self._prefixes[prefix]
diff --git a/pint/testsuite/test_unit.py b/pint/testsuite/test_unit.py
index 2156bbafd..1cca93cec 100644
--- a/pint/testsuite/test_unit.py
+++ b/pint/testsuite/test_unit.py
@@ -1043,3 +1043,8 @@ def test_alias(self):
         # Define against unknown name
         with pytest.raises(KeyError):
             ureg.define("@alias notexist = something")
+
+    def test_prefix_offset_units(self):
+        ureg = UnitRegistry()
+        with pytest.raises(errors.OffsetUnitCalculusError):
+            ureg.parse_units("kilodegree_Celsius")