diff --git a/synapse/app/_base.py b/synapse/app/_base.py
index 46cf2fb098..109b1e2fb5 100644
--- a/synapse/app/_base.py
+++ b/synapse/app/_base.py
@@ -282,9 +282,12 @@ def start(hs, listeners=None):
 
         # We now freeze all allocated objects in the hopes that (almost)
         # everything currently allocated are things that will be used for the
-        # rest of time. Doing so means less work each GC (hopefully)
-        gc.collect()
-        gc.freeze()
+        # rest of time. Doing so means less work each GC (hopefully).
+        #
+        # This only works on Python 3.7
+        if sys.version_info >= (3, 7):
+            gc.collect()
+            gc.freeze()
     except Exception:
         traceback.print_exc(file=sys.stderr)
         reactor = hs.get_reactor()