diff --git a/synapse/storage/data_stores/main/events.py b/synapse/storage/data_stores/main/events.py
index da1529f6ea..bd670f0022 100644
--- a/synapse/storage/data_stores/main/events.py
+++ b/synapse/storage/data_stores/main/events.py
@@ -1053,6 +1053,13 @@ class EventsStore(
         if self.hs.config.redaction_retention_period is None:
             return
 
+        if self.db.updates.has_completed_background_update(
+            "redactions_have_censored_ts_idx"
+        ):
+            # We don't want to run this until the appropriate index has been
+            # created.
+            return
+
         before_ts = self._clock.time_msec() - self.hs.config.redaction_retention_period
 
         # We fetch all redactions that:
diff --git a/synapse/storage/data_stores/main/schema/delta/56/redaction_censor2.sql b/synapse/storage/data_stores/main/schema/delta/56/redaction_censor2.sql
index 49ce35d794..6c36bd5468 100644
--- a/synapse/storage/data_stores/main/schema/delta/56/redaction_censor2.sql
+++ b/synapse/storage/data_stores/main/schema/delta/56/redaction_censor2.sql
@@ -18,5 +18,5 @@ ALTER TABLE redactions ADD COLUMN received_ts BIGINT;
 INSERT INTO background_updates (update_name, progress_json) VALUES
   ('redactions_received_ts', '{}');
 
-INSERT INTO background_updates (update_name, progress_json) VALUES
-  ('redactions_have_censored_ts_idx', '{}');
+INSERT INTO background_updates (update_name, progress_json, depends_on) VALUES
+  ('redactions_have_censored_ts_idx', '{}', 'redactions_have_censored_idx');