diff --git a/grudge/symbolic/operators.py b/grudge/symbolic/operators.py
index b47611d7acdac3538bc4247952f78c42c090167e..b95575f6ee1dd21c91fb26d43c8f158f20f9c427 100644
--- a/grudge/symbolic/operators.py
+++ b/grudge/symbolic/operators.py
@@ -724,6 +724,9 @@ def norm(p, arg, dd=None):
                 prim.fabs(arg * MassOperator()(arg)))
 
         if isinstance(norm_squared, np.ndarray):
+            if len(norm_squared.shape) != 1:
+                raise NotImplementedError("can only take the norm of vectors")
+
             norm_squared = norm_squared.sum()
 
         return prim.sqrt(norm_squared)
@@ -732,6 +735,9 @@ def norm(p, arg, dd=None):
         result = NodalMax(dd_in=dd)(prim.fabs(arg))
 
         if isinstance(result, np.ndarray):
+            if len(result.shape) != 1:
+                raise NotImplementedError("can only take the norm of vectors")
+
             from pymbolic.primitives import Max
             result = Max(result)