Odegaard, visibly in pain, sought assistance to leave the field and had to be replaced after injuring his ankle in the second half of Norway's Nations League victory against Austria in Oslo earlier this month.
The 25-year-old missed Arsenal's North London derby win over Tottenham and is now set for an unspecified spell on the sidelines, with a trip to champions Man City on Sunday - live on .
Speaking ahead of Thursday's Champions League opener at Atalanta, Arteta said: "After recent scans the scans showed that he's got some damage especially on one of the ligaments in the ankle. It's something quite significant so we're going to lose him for a while."
Arsenal will be boosted by the return of Declan Rice in midfield on Sunday after serving his league suspension, but they remain without Mikel Merino.
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' Sam Blitz:
Arsenal have one player in the team they cannot afford to be without and that is captain Martin Odegaard.
The Norwegian midfielder is the heartbeat of the team and his world-class levels both with and without the ball are not only crucial to Mikel Arteta's side, but also impossible to find elsewhere in the team.
Odegaard was the most creative player in the Premier League last season, with the Arsenal captain topping the expected assist tally of 11.17. The only player who got close to that mark was team-mate Bukayo Saka, who got 11.
But it is his role in Arsenal's pressing is where Odegaard is so vital. No player won more possessions in the final third than him last season, while only five players have managed more pressures leading to a turnover than the Gunners midfielder.
It is not an ideal situation for Arsenal, who have away trips to Atalanta and then Premier League champions Man City in the next four days.
They have already dropped points to Brighton this season and may not want any more slip-ups in this unforgiving title race with Man City.
Arsenal's upcoming fixturesAtalanta (A) - Champions League - Thursday September 19
Man City (A) - Premier League - Sunday September 22 - live on
Bolton (H) - Carabao Cup - Wednesday September 25 - live on
Leicester (H) - Premier League - Saturday September 28
PSG (H) - Champions League - Tuesday October 1
Southampton (H) - Premier League - Saturday October 5
Click here for all of Arsenal's fixtures...