The bug affects the Windows, Android, and iOS clients, but Skype for Mac and the touch-optimized Skype for Windows 8.1 app seem to be unaffected.
Skype confirmed to VentureBeat that they are aware of the problem and are working on a fix.
What's annoying about this issue is that it's hard for the end user to solve the problem. Deleting the chat history doesn't fix the problem because the client downloads it as soon as it is reconnected to the web and the client crashes again. One suggested fix is to get the person/prankster who sent you the message to delete it, and then install an older version of the client.
Whatever you do, don't send this as a joke to others because it's an intensely frustrating headache for the user to fix, and could knock them offline until Skype rolls out a patched client.