After Rooney was omitted from the United team to face Chelsea in their FA Cup quarter-final replay, Sir Alex Ferguson revealed the striker had suffered the injury while on international duty with England in Montenegro last week.
The United boss told ITV Sport: "He got a groin injury playing for England and wasn't 100 per cent yesterday and there's no point risking players with groin injuries because it could exacerbate itself and he could be out for weeks.
"So hopefully he'll be ready for next Monday's game.''
Rooney played the full 90 minutes and scored as England drew 1-1 in Podgorica.
United entertain City next Monday (April 8) in the Premier League. If they win, they will be virtually assured of reclaiming the title from their local rivals.