diff --git a/addons/sms/static/src/js/message.js b/addons/sms/static/src/js/message.js
index f800563fd72..b5463ae9f8f 100644
--- a/addons/sms/static/src/js/message.js
+++ b/addons/sms/static/src/js/message.js
@@ -32,6 +32,14 @@ Message.include({
         });
         return this._smsStatus;
     },
+    /**
+     * Whether message has nay SMS-related notification
+     *
+     * @returns {boolean}
+     */
+    hasSmsData: function () {
+        return !!(this._smsIds && (this._smsIds.length > 0));
+    },
     /**
      * Does the message contains at least one SMS failure
      *
diff --git a/addons/sms/static/src/xml/thread.xml b/addons/sms/static/src/xml/thread.xml
index b01524ba609..a28e70f0fa7 100644
--- a/addons/sms/static/src/xml/thread.xml
+++ b/addons/sms/static/src/xml/thread.xml
@@ -3,7 +3,7 @@
 
      <t t-extend="mail.widget.Thread.Message">
         <t t-jquery=".o_thread_tooltip_container" t-operation="after">
-            <span t-if="message.getType() === 'sms' and options.displaySmsIcons" class="o_thread_sms_tooltip_container">
+            <span t-if="message.getType() === 'sms' and message.hasSmsData() and options.displaySmsIcons" class="o_thread_sms_tooltip_container">
                 <t t-set="thread_icon_class" t-value="'o_thread_sms_tooltip o_thread_message_sms o_thread_message_sms_' + message.getSmsStatus()" />
                 <i t-attf-class="o_thread_sms_tooltip o_thread_message_sms o_thread_message_sms_#{message.getSmsStatus()} #{message.isError() ? 'o_thread_message_sms_error' : ''} fa fa-comment"
    t-att-data-message-id="message.getID()"/>