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.
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."
