Mkhitaryan fractured the metatarsal in his right foot in last Wednesday's Carabao Cup defeat by Tottenham and was replaced at half-time. He missed the win against Burnley at the weekend.
Arsenal said the Armenian playmaker is "expected to return to full training in six weeks".
Mkhitaryan has been a regular under Unai Emery and has scored four Premier League goals this season.
The 29-year-old will miss key league games against Liverpool, Chelsea and Manchester City as Arsenal continue their pursuit of a top-four place.
Mkhitaryan arrived at the Emirates Stadium almost a year ago as part of the swap deal that took Alexis Sanchez to Manchester United.