The midfielder was forced off before half-time after a heavy collision with Crysencio Summerville, in a match decided by goals from Declan Rice and Bukayo Saka.
Odegaard attempted to continue after the incident but was replaced by Martin Zubimendi, with Mikel Arteta later admitting concern over the challenge. "It did not look good at the time," the Arsenal manager said.
"Martin wanted to carry on, but we had to take precautions. He is an important player for us, and we need to make sure he recovers properly."
The club have since confirmed that Odegaard suffered a medial collateral ligament (MCL) injury to his left knee. As a result, he has pulled out of Norway's upcoming fixtures against New Zealand and Israel and will remain at Arsenal's Sobha Realty Training Centre during the international break for further assessment and treatment.
According to medical guidance published by Physio Scout, recovery from an MCL injury can range from one to three weeks for a minor issue, three to six weeks for a moderate one, and up to ten weeks for a severe tear, though a grade three injury "appears unlikely" in Odegaard's case.
The setback marks Odegaard's third injury in the opening ten games of the campaign, a frustrating spell that has disrupted his rhythm in midfield. His absence is another blow to Arsenal, who are already without Kai Havertz, Gabriel Jesus, Piero Hincapie and Noni Madueke.
With Eberechi Eze and teenager Ethan Nwaneri ready to step in, Arteta will be hoping his captain's latest layoff proves short as Arsenal aim to maintain their strong start to the season.
Manchester City secured a second successive Premier League victory at home against Sunderland, Chelsea were held scoreless away to Bournemouth while Tottenham managed to beat Brentford.
Aston Villa delivered a major jolt to the Premier League title race as Emiliano Buendía struck deep into stoppage time to seal a 2-1 win over Arsenal on Saturday.
David Moyes urged Everton to stay on the front foot as they prepare for Saturday's Premier League meeting with Nottingham Forest at Hill Dickinson Stadium, where Sean Dyche made his first return since leaving the club nearly a year ago.
Mikel Arteta has said that Aston Villa's blistering run of form has made them genuine contenders in the Premier League title race, as Arsenal prepare for a high-stakes trip to Villa Park.
