I'm currently watching a bbc documentary called Tankies: Tank Heroes of World War II. In it there's a short clip of Rommel going over plans in the desert and he appears to have a black eye and cut lip!
Has there ever been a reason given for it?
I found this source
It mentions him receiving facial injuries from a shell fragment at some point. I'm not positive it was the same event but it seems reasonable given the injuries you described. Another injury could have been due to his car getting strafed by an aircraft and the ensuing accident. It fractured his skull and hurt the left side of his face(including glass cuts). If you've seen the movie "valkyrie" a very similar scene is in it, however the main character lost an eye rather than it being bruised. It would really help to know when the clip was from to actually pinpoint the injury.