The France international picked up the injury in Saturday's 2-1 defeat to Chelsea and could be joined on the sidelines by Mikel Arteta, who faces a fitness test on an ankle knock tomorrow.
"Arteta will have a test tomorrow morning," Arsene Wenger said. "We will make the decision then whether we include him in the squad or not. He has an ankle injury.
"We lost Diaby, who has a thigh strain. He is definitely out for three weeks as well. Apart from Diaby and Arteta, everyone came through well."
Jack Wilshere sharpened his fitness with an Under-21s game yesterday and
The 20 year-old has struggled with an ankle injury suffered prior to last season but stepped up his comeback by playing 63 minutes of the Gunners' under-21 game at West Brom.
Wilshere came through the match unscathed and Burton was pleased with the midfielder's performance.
"It's like all players when they come back for their first game: they realise how difficult and tough it is," he said.
"You always have to make that first step, and he has done that and that is fantastic.
"He is a quality player, it is great for the club that he has taken that first step on the road towards getting back into the first team.
"I think he is delighted to have been back on the pitch, as we all are.
"It is a start, now he just needs to keep working hard to play the football we know he is capable of playing, which we know is very exciting.
"When he runs with the ball, it is very close to him and as he runs he always has his head up and is looking for opportunities to play people in.
"What you can't duplicate in training is that match sharpness and players coming in at you, so he will have benefited from that in this match."
Wenger, meanwhile, wants his side to make amends for Saturday's defeat to Chelsea when the Gunners take on Olympiakos in the Champions League.
The north Londoners saw a successful start to the season abruptly halted at the weekend as they fell to a 2-1 defeat to Chelsea at the Emirates Stadium.
Arsenal sit seven points shy of the Premier League leaders as a result, but attention now turns to their Champions League campaign.
Wenger's side takes on the Greek champions tomorrow and the Frenchman wants to see an improved performance in the Group B encounter.
"The players are focused and disappointed that we lost the game," the Arsenal manager said.
"They are still down of course, but we have a Champions League game in front of us at home and we want to put things right.
"There were a lot of positives in that game as well, what was not good is easy to correct.
"I believe the championship is long, but we have to make sure the Champions League is long as well.
"It is about how we respond. I am impressed by the mentality of my team, but the mentality is as well about how you respond to disappointment.
"I am confident we will, but that is what we want to show tomorrow."
Arsenal will be hoping to make it two wins from two Group B games tomorrow, having returned from Montpellier with three points on matchday one.
Olympiakos, who Arsenal also faced in the group stage last year, are without a point after losing their opener at home to Schalke and Wenger knows tomorrow's clash at the Emirates provides a chance to take a stranglehold on the group.
"Olympiakos are already in a position where their backs are to the wall because they have lost at home and in this Champions League when you lose at home it is very difficult," the Frenchman said.
"They are highly motivated to know they have to give everything to make it through. They are experienced and basically it is the same team (as it was) at the back of last season.
"I think they had a difficult start against Marseille and after became stronger and stronger through the competition last year.
"It looks similar this year, they had a difficult start at home against Schalke and if you analyse their team it is 90 per cent the same as last season."