One has to wonder how a major bug like this one slipped through the testing cracks.
Look for the option to block updates under Computer Configuration\Administrative Templates\Microsoft Office 2013 (Machine)\Updates.
Double click on Enable Automatic Upgrade and choose Disabled, then click Apply and close the dialog.
For Office 365 for business subscribers According to KB article 3097292 (How do I keep on running Office 365 Pro Plus 2013), Office 365 Pro Plus subscribers navigates in registry editor to the key: The key entry works also for Office 365 Business, which is the version of Office that comes with the Office 365 Business and Office 365 Business Premium plans.
Microsoft’s KB article KB097292 also describes how to block the notification using group policy templates for Office 2013.
Searching the web shows several forum posts (here) where users are complaining about this behavior and searching ways to block the notification.
A Microsoft forum moderator posted here a few details when and why the notification will be shown for Office 365 for business subscribers: Users who purchased an Office 365 for home subscription, such as Office 365 Home, seeing this notification, should upgrade to Office 2016.
A bug that stops any Office application dead in its track is quite serious; Office administrators and users who have not installed the patch yet may want to consider skipping it until the issue is resolved.
One Note 2016 users who require Sync may want to try installing the patch.
The company provides removal instructions for the update.