Authentication Required Pop Up

Over the last couple of days a pop up has appeared asking for a password and username to log into my site.
It never used to. I don’t know if this is a hack or a genuine wordpress safety thing, but it seems more like a hack.
It says for more info go to webhostingstatus.com where it gives you the password.

To me this seems like pointless security if it simply gives the password to anyone who looks at the site!

I’ve tried searching the forums for an answer.
Some people seem to be saying there is code hidden in php files. I’ve had a look at all my plugin ones and a few others that have been mentioned and found nothing.
Others say to update wordpress, but I was already on the latest version. I re-installed to see if that worked.

This first appeared two days ago. I was logged in, with a post editor open. I clicked to go to the Dashboard home and this pop up appeared and I was logged out.
I had not installed any new plugins or anything like that. The page had simply been sitting open for a while.