The 25-year-old forward was stretchered off in Arsenal's 1-0 win over Queens Park Rangers last weekend and played no part in the club's extraordinary 7-5 victory over Reading in the League Cup on Tuesday.
"Reading was an irrational game. Some of the players still have heavy legs. [There will be] no Wojciech [Szczesny], no [Kieran] Gibbs, no [Abou] Diaby as well. Gervinho is out for three weeks," Wenger told reporters.
In addition to Saturday's match against United, the Ivory Coast international will miss the club's Champions League group match against Schalke 04 and Premier League encounters with Fulham and Tottenham Hotspur.
Gervinho has scored three times in seven Premier League starts this season, having featured as a central striker rather than on the wing where he played for much of his debut season at the club.
Theo Walcott is another player that Wenger said he would like to see play as a central striker in the future but he wants his contract situation settled by Christmas.
The England forward's current deal is up in 2013, but the 23-year-old gave a timely reminder his scoring prowess with two goals in Tuesday's League Cup thriller.
The French boss sang the striker's praises after the match and on Thursday reiterated his desire to keep hold of the player.
"There is urgency. I want it resolved by Christmas," Wenger said.
"His right position is through the middle in the future. We saw that in the game on Tuesday night. The positions on the flanks are changing, you have to do a lot of defending."
Arsenal face United at Old Trafford on Saturday. They were thrashed 8-2 thrashing by the same opponents in the same fixture last season.
The North London club are currently sixth in the Premier League, six points behind United in second.
