diff --git a/theme/afterburner/style/afterburner_dock.css b/theme/afterburner/style/afterburner_dock.css
index 2d25526f0ad..ff6dab3cd10 100644
--- a/theme/afterburner/style/afterburner_dock.css
+++ b/theme/afterburner/style/afterburner_dock.css
@@ -124,4 +124,10 @@ Docked Item Panel
     overflow:auto;
     width:auto; /* adds scroll to dock panel */
 }
-#dockeditempanel .dockeditempanel_bd .block_navigation .block_tree li {overflow:visible;}
\ No newline at end of file
+#dockeditempanel .dockeditempanel_bd .block_navigation .block_tree li {overflow:visible;}
+
+/* Hide the move icon for blocks which are docked */
+#dock .editing_move,
+#dock .moodle-core-dragdrop-draghandle {
+    display: none;
+}