The 23-year-old picked up a thigh strain during the first half of Wednesday's 2-2 fightback draw against Liverpool and was initially ruled out for three weeks.
But he now faces twice as long on the sidelines and is set to miss both Champions League last-16 ties against Bayern Munich.
Wenger told reporters on Friday the development had prompted his deadline-day move for Spain full-back Nacho Monreal.
"We expected two to three weeks; now it will be four to six so we were in a
position where we had to make a quick decision. That explains our buy," Wenger said.
"I believe Gibbs will be out for the Champions League. From six weeks it can easily go to eight (before he is competitive again) and that means two months in a very decisive period so it is vital to have another left-back.
Montreal will miss the double-header against the Germans having already featured in the competition for Malaga, leaving Andre Santos likely to take the shirt.
The Brazilian's recent performances have come under criticism from supporters but Wenger believes he will benefit from fresh competition.
"Santos could have a key role," Wenger added. "Maybe people speak that he had a difficult game (against Liverpool) but he lacks competition.
"He is a stamina type of player and gets sharper through competition. If you watch the game again you will be less critical. He did some good things."