diff --git a/apps/emqx_management/src/emqx_mgmt.erl b/apps/emqx_management/src/emqx_mgmt.erl
index 35908d3bd..bc194f03e 100644
--- a/apps/emqx_management/src/emqx_mgmt.erl
+++ b/apps/emqx_management/src/emqx_mgmt.erl
@@ -711,5 +711,19 @@ call_conn(ConnMod, Pid, Req) ->
         exit:R when R =:= shutdown; R =:= normal ->
             {error, shutdown};
         exit:{R, _} when R =:= shutdown; R =:= noproc ->
-            {error, shutdown}
+            {error, shutdown};
+        exit:{{shutdown, _OOMInfo}, _Location} ->
+            {error, shutdown};
+        exit:timeout ->
+            ?SLOG(
+                warning,
+                #{
+                    msg => "call_client_connection_process_timeout",
+                    request => Req,
+                    pid => Pid,
+                    module => ConnMod,
+                    stacktrace => erlang:process_info(Pid, current_stacktrace)
+                }
+            ),
+            {error, timeout}
     end.
diff --git a/apps/emqx_management/src/emqx_mgmt_api_clients.erl b/apps/emqx_management/src/emqx_mgmt_api_clients.erl
index dd65c1245..262faf87f 100644
--- a/apps/emqx_management/src/emqx_mgmt_api_clients.erl
+++ b/apps/emqx_management/src/emqx_mgmt_api_clients.erl
@@ -1232,6 +1232,8 @@ list_client_msgs(MsgType, ClientID, QString) ->
                         code => 'NOT_IMPLEMENTED',
                         message => <<"API not implemented for persistent sessions">>
                     }};
+                {error, Reason} ->
+                    ?INTERNAL_ERROR(Reason);
                 {Msgs, Meta = #{}} when is_list(Msgs) ->
                     format_msgs_resp(MsgType, Msgs, Meta, QString)
             end
diff --git a/changes/ce/fix-12814.en.md b/changes/ce/fix-12814.en.md
new file mode 100644
index 000000000..f84025561
--- /dev/null
+++ b/changes/ce/fix-12814.en.md
@@ -0,0 +1,4 @@
+Handle several errors in `/clients/{clientid}/mqueue_messages` and `/clients/{clientid}/inflight_messages` APIs:
+
+- Internal timeout, which means that EMQX failed to get the list of Inflight/Mqueue messages within the default timeout of 5 s. This error may occur when the system is under a heavy load. The API will return 500 `{"code":"INTERNAL_ERROR","message":"timeout"}` response and log additional details.
+- Client shutdown. The error may occur if the client connection is shutdown during the API call. The API will return 404 `{"code": "CLIENT_SHUTDOWN", "message": "Client connection has been shutdown"}` response in this case.