The centre-back, who was assessed by the club's medics on Monday, was withdrawn after 36 minutes of the qualifier in Germany as the World Cup holders won their 10th straight game in the qualification stages for next summer's tournament in Russia.
Mustafi, who has made five league appearances for the Gunners so far this season, pulled up in the build-up to Azerbaijan's equalising goal, and he left the field after treatment, replaced by Matthias Ginter.
Arsene Wenger's side travel to Vicarage Road in their next league match on October 14, and with Laurent Koscielny and Calum Chambers both recovering from knocks, the French boss is struggling for defensive options ahead of the Watford clash.
According to 'Sky Sports' Germany's medical team were concerned that the defender would be a doubt for their next international break, but are waiting for updates from Arsenal over the next few days.
After the game, Germany coach Joachim Loew said: "It doesn't look good, it looks like he had torn a ligament. We're waiting for a full diagnosis, but it looks like he will be out for a while."