tommip on "New broken URLs show up in Search Console"

I'm very puzzled. I received a notification from Google Search Console (formerly Webmaster Tools) stating my WP site recently had a significant increase in 404 errors.

There are numerous new URL's crawled by Google but the URL's in all of them are mixed up so that the correct URL has the domain in the end of it.

Eg:
mydomain.com/page1/mydomain.com
mydomain.com/page2/mydomain.com
Also the domain itself is listed as 404: mydomain.com (without http or anything).

Any ideas what could cause these URL's to be visible to Google's bot? Looks like only some of the pages have these "duplicate" URL's.
This problem just appeared out of nowhere and is affecting the site visibility on Google.

All the correct URL's (eg. mydomain.com/page2/) are working fine. These weird URL's can't be found from the sitemaps. I haven't made any changes to the URL structures or settings. No updates either, unless the server provider has done something without my knowledge.