The 26-year-old became the first player in Premier League history to be substituted in the first half in three consecutive games after collision with West Ham's Crysencio Summerville.
According to a report from BBC Sport, Mikel Arteta will be without his skipper for some time, and Odegaard won’t be back until late November at the earliest.
Odegaard could now miss a crucial period for Arsenal as they prepare to face Tottenham, Bayern Munich, and Chelsea before he is projected to return.
Speaking about Odegaard’s recent injury issues, Arteta said: “We haven't had him since the start of the season for one reason or the other. The shoulder twice and then this injury.
“We'll have to wait and see the extent of that injury, and we'll find solutions, but obviously he's our captain and is a player that gives us a completely different dimension with the things that he can do, especially in attacking.”