Rooney was carried off the pitch on a stretcher in injury time after getting caught by Hugo Rodallega.
"He's got a bad one. He's gone to hospital," Ferguson said. "It looks as he'll be out for maybe four weeks."
"I don't know what happened. I think the player must have followed through after he shot."
The injury is likely to keep Rooney out of England's first two World Cup qualifiers against Moldova on Sept. 7 and Ukraine on Sept. 11.
He will also likely miss the beginning of United's Champions League campaign and potentially the away game against Liverpool in the Premier League on Sept. 23.