Arsene Wenger confirmed the news when speaking ahead of his team's Champions League Group B match against Olympiacos at Emirates Stadium on Wednesday.
"Diaby is out for three weeks with a thigh injury," Wenger told a news conference. "(Mikel) Arteta to have test tomorrow."
The injury-prone Diaby had to be substituted early in the Premier League match against Chelsea on Saturday which Arsenal lost 2-1, their first defeat of the season.
Better news for Wenger was that 20-year-old midfielder Jack Wilshere played an Under-21 game on Monday, his first competitive appearance after missing 14 months through injury.
"You always have to make that first step, and he has done that today and that is fantastic," reserve team coach Terry Burton told the club's website.
"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."
Wenger wants his side to make amends for Saturday's defeat to Chelsea when they play Olympiacos.
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 Emirates Stadium. Arsenal sit seven points shy of the Premier League leaders as a result, but attention now turns to their European campaign.
The Frenchman said: "The players are focused and disappointed that we lost the game. 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."
He added: "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, having returned from Montpellier with three points on matchday one.
Olympiacos, 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 Wednesday's clash at the Emirates provides a chance to take a stranglehold on the group.
He said: "Olympiacos 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. They are highly motivated to know they have to give everything to make it through."
The Athens club will be will have to do without top scorer Rafik Djebbour after the Algerian failed to shake off a thigh injury.
The 28-year-old striker sat out his team's 1-0 league win over Atromitos Athinon on Saturday in the hope that he could return for the midweek match, but has not travelled to London.