Arsenal are now unbeaten in their last four Premier League meetings with Manchester City.
Arsenal finished third in the UEFA Champions League group stage, only behind Liverpool and Barcelona.
Arsenal came back from 0-1 down to win 2-1 against Tottenham, closing the gap to Liverpool to four points for the time being.
Arsenal are still five points behind league leaders Liverpool, and have played two more games.
Mikel Arteta praised his Arsenal team for how they have coped with a punishing defensive injury crisis as he prepares his men to face Monaco in the Champions League.
Hakan Calhanoglu fired Inter Milan to a 1-0 win over Arsenal on Wednesday to continue their unbeaten start in the Champions League and inflict a first defeat on the Gunners in this year's revamped tournament.
Mikel Arteta's men have now picked up just one point in their past three games as their title push quickly runs out of steam.
The Spaniard said Odegaard would not be ready for this weekend but the situation will be reassessed ahead of next week's games against Shakhtar Donetsk, in the Champions League, and Liverpool.
Leandro Trossard has come in for the top-flight games missed by Martin Odegaard, as well as the Champions League win over Paris Saint-Germain this week.
Arsenal manager Mikel Arteta said he still "loves" Manchester City boss Pep Guardiola despite last weekend's bad-tempered top-of-the-table clash.