The winger, along with Andre Santos, will miss Arsene Wenger's side's fixture against the French champions but Kieran Gibbs and Gervinho returnTheo Walcott will miss Arsenal's Champions League Group B clash against Montpellier on Wednesday evening with a shoulder injury.
The winger fell awkwardly following a challenge from Michael Dawson during Arsenal's 5-2 victory over Tottenham on Saturday but was able to complete the match after receiving treatment.
Arsene Wenger has confirmed the 23-year-old will be sidelined for the "short term" and will subsequently sit out Arsenal's tie against the French champions at the Emirates, while Andre Santos will also miss out through injury.
Wenger also revealed Kieran Gibbs and Gervinho are fit enough to be included in Arsenal's squad after recovering from injury.
With four games played in the Champions League, Arsenal sit second in Group B on seven points and trail leaders Schalke by a single point. Olympiakos sit third having won two and lost two so far, while Montpellier are yet to register a victory but secured a draw against Schalke last month.