The Bosnia worldwide was forced off during Wednesday's pre-season win over London rivals Chelsea in Dublin after a clash with Victor Moses.
The Bosnian worldwide limped off in the 70th minute and was replaced by Ainsley Maitland-Niles as Arsenal went on to beat our London rivals on penalties at the Aviva Stadium in Dublin.
The "Gunners" begin their campaign at the Emirates against reigning Premier League champions Manchester City, before facing Chelsea at Stamford Bridge the following weekend. Will be out for 8-10 weeks, ' a statement on Arsenal's website read.
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"I'm very pleased Alex has signed a new contract with us", he said in the club's announcement.
The North Londoners also confirmed that Aaron Ramsey "developed tightness in his right calf" prior to the game in the Republic of Ireland, but will aim to return to training next week.
Arsenal beat Maurizio Sarri's Chelsea on Wednesday on penalties after the game ended 1-1 after normal time.
Before kicking off their Premier League season, Arsenal take on Lazio in their final pre-season friendly on Saturday.