diff --git a/cubed/primitive/blockwise.py b/cubed/primitive/blockwise.py
index 1cfc83a97..2190deeec 100644
--- a/cubed/primitive/blockwise.py
+++ b/cubed/primitive/blockwise.py
@@ -687,6 +687,15 @@ def make_blockwise_key_function(
         False,
     )
 
+    for axes, (arg, _) in zip(concat_axes, argpairs):
+        for ax in axes:
+            if numblocks[arg][ax] > 1:
+                raise ValueError(
+                    f"Cannot have multiple chunks in dropped axis {ax}. "
+                    "To fix, use a reduction after calling map_blocks "
+                    "without specifying drop_axis, or rechunk first."
+                )
+
     def key_function(out_key):
         out_coords = out_key[1:]
 
diff --git a/cubed/tests/primitive/test_blockwise.py b/cubed/tests/primitive/test_blockwise.py
index 06eaa624b..c8a01b8e3 100644
--- a/cubed/tests/primitive/test_blockwise.py
+++ b/cubed/tests/primitive/test_blockwise.py
@@ -266,11 +266,11 @@ def test_make_blockwise_key_function_contract():
     func = lambda x: 0
 
     key_fn = make_blockwise_key_function(
-        func, "z", "ik", "x", "ij", "y", "jk", numblocks={"x": (2, 2), "y": (2, 2)}
+        func, "z", "ik", "x", "ij", "y", "jk", numblocks={"x": (2, 1), "y": (1, 2)}
     )
 
     graph = make_blockwise_graph(
-        func, "z", "ik", "x", "ij", "y", "jk", numblocks={"x": (2, 2), "y": (2, 2)}
+        func, "z", "ik", "x", "ij", "y", "jk", numblocks={"x": (2, 1), "y": (1, 2)}
     )
     check_consistent_with_graph(key_fn, graph)
 
@@ -290,10 +290,10 @@ def test_make_blockwise_key_function_contract_0d():
     func = lambda x: 0
 
     key_fn = make_blockwise_key_function(
-        func, "z", "", "x", "ij", numblocks={"x": (2, 2)}
+        func, "z", "", "x", "ij", numblocks={"x": (1, 1)}
     )
 
-    graph = make_blockwise_graph(func, "z", "", "x", "ij", numblocks={"x": (2, 2)})
+    graph = make_blockwise_graph(func, "z", "", "x", "ij", numblocks={"x": (1, 1)})
     check_consistent_with_graph(key_fn, graph)
 
 
diff --git a/cubed/tests/test_core.py b/cubed/tests/test_core.py
index a40702373..715b81b77 100644
--- a/cubed/tests/test_core.py
+++ b/cubed/tests/test_core.py
@@ -235,6 +235,28 @@ def func(x, y):
     assert_array_equal(c.compute(), np.array([[[12, 13]]]))
 
 
+def test_map_blocks_drop_axis_chunking(spec):
+    # This tests the case illustrated in https://docs.dask.org/en/stable/generated/dask.array.map_blocks.html
+    # Unlike Dask, Cubed does not support concatenating chunks, and will fail if the dropped axis has multiple chunks.
+
+    def func(x):
+        return nxp.sum(x, axis=2)
+
+    an = np.arange(8 * 6 * 2).reshape((8, 6, 2))
+
+    # single chunk in axis=2 works fine
+    a = xp.asarray(an, chunks=(5, 4, 2), spec=spec)
+    b = cubed.map_blocks(func, a, drop_axis=2)
+    assert_array_equal(b.compute(), np.sum(an, axis=2))
+
+    # multiple chunks in axis=2 raises
+    a = xp.asarray(an, chunks=(5, 4, 1), spec=spec)
+    with pytest.raises(
+        ValueError, match=r"Cannot have multiple chunks in dropped axis 2."
+    ):
+        cubed.map_blocks(func, a, drop_axis=2)
+
+
 def test_map_blocks_with_non_cubed_array(spec):
     a = xp.arange(10, dtype="int64", chunks=(2,), spec=spec)
     b = np.array([1, 2], dtype="int64")  # numpy array will be coerced to cubed