The Gunners have been without their star playmaker for a number of weeks after it was revealed he was initially carrying a hip issue.
However, he was forced to sit out the games against Newcastle, Sevilla and Burnley recently due to concussion protocol.
Odegaard was hit by a ball in the face during training in the lead-up to the trip to St. James' Park.
The protocol demands any player affected by a concussion sit out six days of action and be free of symptoms before returning.
Arsenal have also taken the decision to withdraw Odegaard from Norway duty this week, which is said to be related to fully resting his hip injury.
It is expected that he'll be back after the international break, however.
Norway face Scotland in a Euro 2024 qualification dead-rubber before a friendly against the Faroe Islands.
Arsenal travel to Brentford in just under a fortnight's time while also worrying over injuries to Gabriel Jesus, Ben White, Emile Smith Rowe and Thomas Partey.