The Brazilian defender, who made the switch to the Emirates Stadium from Villarreal in the last transfer window, hobbled off shortly before half-time of Wednesday's 2-1 Premier League victory at QPR.
As well as being absent for Monday's FA Cup quarter-final tie against Manchester United, Gabriel could also miss Premier League matches against West Ham, Newcastle United and Liverpool as well as the UEFA Champions League last 16 second leg tie at Monaco.
The FA Cup clash against United will see forward Danny Welbeck return to Old Trafford for the first time since he left to join Arsenal last September.
And Wenger has been thrilled with his impact since arriving, adding: "He's [Welbeck] very important and has played many, many games.
"He's an exceptional footballer who will have a great future here. I'm very, very happy I bought him."
The Frenchman is also expecting a tight contest between the joint most successful teams in the history of the FA Cup - Arsenal's 2014 victory levelling things up at 11 apiece.
"I don't believe too much in history," he continued. "At the moment we are doing very well away from home so it's down to our effort.
"We are the holders of the FA Cup and we want to keep it. The cup is about giving it all on the day and we'll do that on Monday.
"It's a special intensity because it's between two teams with a chance of winning. We're focused on the FA Cup."
Wenger also confirmed that late checks will be given to Nacho Monreal and goalkeeper Wojciech Szczesny.
