Mkhitaryan fractured the metatarsal in his right foot on 19 December during the 2-0 defeat to Tottenham Hotspur in the quarter-final of the Carabao Cup.
Arsenal say the Armenian playmaker is expected to return to full training in six weeks.
Mkhitaryan, who played at Borussia Dortmund before moving to Manchester United for 42 million euros in 2016, has been a regular under Unai Emery and has scored four Premier League goals this season.
The 29-year-old will miss league games against Brighton, Fulham, West Ham, Cardiff City, Huddersfield, Chelsea and Manchester City before he returns to training in the middle of February.
Mkhitaryan arrived at the Emirates Stadium almost a year ago as part of the swap deal that took Alexis Sanchez to Manchester United.