diff --git a/web/utils/tooltip-utils.js b/web/utils/tooltip-utils.js
--- a/web/utils/tooltip-utils.js
+++ b/web/utils/tooltip-utils.js
@@ -409,12 +409,33 @@
   }, [addReply, item.messageInfo.type, messageInfo, threadInfo]);
 }
 
+const copiedMessageDurationMs = 2000;
 function useMessageCopyAction(
   item: ChatMessageInfoItem,
 ): ?MessageTooltipAction {
   const { messageInfo } = item;
 
   const [successful, setSuccessful] = React.useState(false);
+  const timeout = React.useRef();
+
+  const onSuccess = React.useCallback(() => {
+    if (timeout.current) {
+      clearTimeout(timeout.current);
+    }
+    setSuccessful(true);
+    timeout.current = setTimeout(() => {
+      setSuccessful(false);
+      timeout.current = null;
+    }, copiedMessageDurationMs);
+  }, []);
+
+  React.useEffect(() => {
+    return () => {
+      if (timeout.current) {
+        clearTimeout(timeout.current);
+      }
+    };
+  }, []);
 
   return React.useMemo(() => {
     if (messageInfo.type !== messageTypes.TEXT) {
@@ -424,7 +445,7 @@
     const onClick = async () => {
       try {
         await navigator.clipboard.writeText(messageInfo.text);
-        setSuccessful(true);
+        onSuccess();
       } catch (e) {
         setSuccessful(false);
       }
@@ -434,7 +455,7 @@
       onClick,
       label: successful ? 'Copied!' : 'Copy',
     };
-  }, [messageInfo.text, messageInfo.type, successful]);
+  }, [messageInfo.text, messageInfo.type, onSuccess, successful]);
 }
 
 function useMessageTooltipActions(