Despite scoring the only goal of the game at Old Trafford, the England ace had to leave the pitch after only seven minutes, making way for Carlos Tevez.
"Wayne has done his hamstring," confirmed United boss Alex Ferguson on Thursday.
"It's one of those things, but it's a three-week job I'm afraid. Hopefully it won't be any longer than that."
Injuries
Ferguson, who already missed Rio Ferdinand and Patrice Evra against the Latics, admitted that injuries have taken their toll on his side.
However, the Scotsman is hopeful he can have some players back by next Saturday, when the Red Devils take on Bolton.
"We were carrying injuries throughout the game and that says a lot for the character of the team," he said.
"Tevez limped throughout the second-half, Jonny Evans, Paul Scholes, Ronaldo. They all seemed to be limping about the place.
"In terms of who will be fit for Saturday, we will just have to assess the injuries and do our best against a Bolton team that are very strong themselves. But Darren Fletcher, Anderson, Park Ji-Sung will be fresh, so they will all play."
United have a chance of being top if they grabbed a win at Reebok Stadium, as they trail leaders Liverpool by two points, but have a game in hand.