diff --git a/python/CHANGELOG.rst b/python/CHANGELOG.rst
index c208248e8a..2377707c59 100644
--- a/python/CHANGELOG.rst
+++ b/python/CHANGELOG.rst
@@ -72,8 +72,11 @@
   values with mutations over roots.
   (:user:`benjeffery`, :pr:`3274`, :issue:`3273`)
 
+- Prevent iterating over a ``TopologyCounter``
+  (:user:`benjeffery` , :pr:`3202`, :issue:`1462`)
 
-**Breaking changes** 
+
+**Breaking changes**
 
 - ``ltrim``, ``rtrim``, ``trim`` and ``shift`` raise an error if used on a tree sequence
   containing a reference sequence (:user:`hyanwong`, :pr:`3210`, :issue:`2091`)
diff --git a/python/tests/test_combinatorics.py b/python/tests/test_combinatorics.py
index 97c85af8e8..8073b845df 100644
--- a/python/tests/test_combinatorics.py
+++ b/python/tests/test_combinatorics.py
@@ -635,6 +635,11 @@ def verify_topologies(self, ts, sample_sets=None, expected=None):
                         assert actual_topologies == expected[i][sample_set_indexes]
                     assert actual_topologies == actual_inc_topologies
 
+    def test_no_iterate(self):
+        with pytest.raises(TypeError, match="not iterable"):
+            for _ in tskit.Tree.generate_star(3).count_topologies():
+                pass
+
     def subsample_topologies(self, ts, sample_sets, sample_set_indexes):
         subsample_sets = [sample_sets[i] for i in sample_set_indexes]
         topologies = collections.Counter()
diff --git a/python/tskit/combinatorics.py b/python/tskit/combinatorics.py
index 880ec73675..058f6e633e 100644
--- a/python/tskit/combinatorics.py
+++ b/python/tskit/combinatorics.py
@@ -541,6 +541,12 @@ def __setitem__(self, sample_set_indexes, counter):
         k = TopologyCounter._to_key(sample_set_indexes)
         self.topologies[k] = counter
 
+    def __iter__(self):
+        raise TypeError(
+            "TopologyCounter object is not iterable, "
+            "iterate over '.topologies' instead"
+        )
+
     @staticmethod
     def _to_key(sample_set_indexes):
         if not isinstance(sample_set_indexes, collections.abc.Iterable):