WordPress 3.9 Database Update Infinite Loop

I recently updated my blog’s WordPress version to 3.9. After running the update I received this message upon trying to access the admin panel.

Database Update Required

WordPress has been updated! Before we send you on your way, we have to
update your database to the newest version.

The update process may take a little while, so please be patient.

I am presented then with a button “Update WordPress Database“. When I click the button, after a short pause I am presented with the following message.

Update Complete

Your WordPress database has been successfully updated!

Great. Except that whenever I try to access the admin panel I am re-presented the first message asking me once again to update my database.

Does anybody know of a way out of this infinite loop?

I had that on one of my sites recently (set to auto update core, so not sure if on 3.9 or one of 3.8.*). Flushing cache fixed it — wp cache flush via wp-cli, I imagine other ways would work just as well.