But when I click, there is no message.
Reblogging instead of replying because I know a lot of people are seeing this problem. This happens if you have a message from someone who has since deleted their Tumblr account. I was eventually able to fix mine by going to the inbox from the Tumblr app and deleting it that way.
You are a genius! I’ve had a lot of ghost messages on one of my sub-tumblrs that I could never delete, but I was able to read and delete them in the iPhone app. Just another example of Tumblr quality.