The 25-year-old playmaker initially linked up with the national team carrying a knock from the 1-1 Premier League draw with Brighton & Hove Albion, but he managed to complete the full 90 minutes in Norway's opening Nations League match with Kazakhstan (0-0) last Friday.
Odegaard was once again handed a start in midfield for Norway's encounter against Austria on Monday, but his evening was cut short after he sprained his ankle midway through the second half following a challenge with Christoph Baumgartner.
The Gunners star required treatment on the pitch by Norway physios and looked in some distress as he was consoled by teammate Erling Haaland before being helped off the field and down the tunnel.
Norway were drawing 1-1 with Austria at the time of Odegaard's exit, but they came away with all three points courtesy of Haaland's match-winner 10 minutes from time.
Odegaard to undergo ankle scan on Tuesday
Speaking to reporters after the match, Norway head coach Solbakken delivered a concerning update on Odegaard's condition.
"It looked bad in the dressing room too", said Solbakken. "He didn't have the nerve to continue. It is not certain that Arteta will call me tonight and praise me."
Norway doctor Ola Sand has also shared his views on Odegaard's injury, telling Norwegian news outlet TV2: "He got a small ankle sprain. We will see, maybe we use ultrasound to look at it. If we are unsure, there will be an MRI tomorrow.
"Ankle sprains are difficult to deal with straight away, so we almost have to see how things go forward.
"We will examine him when we are back at the hotel. Maybe we use ultrasound to look at it. If we are unsure, there will be an MRI."
Arsenal could be without four players for Spurs clash
Odegaard has become the second Arsenal player to suffer an injury in this month's international break alongside Italian defender Riccardo Calafiori, who sustained a bizarre calf problem against France and subsequently pulled out of the squad over the weekend.
Calafiori's issue does not appear to be a serious one, but the £42m summer signing from Bologna has emerged as a doubt for Sunday's North London derby and will be assessed ahead of kickoff.
Meanwhile, Mikel Arteta will have to cope without another new recruit in the form of Mikel Merino, as he continues to recover from a shoulder fracture suffered in one of his first training sessions after joining from Real Sociedad.
Declan Rice will also miss the clash with Tottenham as he is to serve a one-match ban following his red card against Brighton prior to the international break.
The absence of Rice, Merino and potentially Odegaard leaves Arsenal light in the midfield department, meaning players including Thomas Partey and Jorginho may be required to step up for the trip to Spurs.