Odegaard picked up a knock during his side's 2-0 Premier League win over West Ham United on Saturday, and although he tried to continue he was eventually replaced by Martin Zubimendi after 30 minutes.
The 26-year-old will miss Norway's World Cup 2026 qualifier against Israel on Saturday, as well as their friendly match against New Zealand on October 14.
In a statement, Arsenal said Odegaard had sustained a medial collateral ligament injury to his left knee.
"Martin will continue to be assessed and treated by our medical team ... during the international window, with the aim of a return to action as soon as possible."
Odegaard's season has been heavily impacted by injuries, with the midfielder having injured his shoulder against Leeds United in August and suffering a recurrence of that injury against Nottingham Forest last month.
