The Norway international suffered a nasty twist during his country's Nations League win over Austria earlier in September, and he was seen on crutches as he boarded a flight back to England the next day.
The extent of Odegaard's issue was not immediately confirmed by club staff, although Norway's team doctor estimated that the midfielder could be absent for around three weeks.
Nevertheless, Arteta refused to rule his skipper out of Sunday's North London derby against Tottenham Hotspur, but as expected, he was missing from the squad for that 1-0 triumph.
The significant swelling on Odegaard's ankle is thought to have prevented initial scans from revealing the full extent of the problem, but the 25-year-old was then sent to a specialist and was absent from team training on Wednesday morning.
Arteta: 'Odegaard injury is big test for Arsenal'
After touching down in Italy for Thursday's Champions League opener against Atalanta BC, Arteta confirmed to the media that Odegaard would be missing for a "while", although he refused to specify how many weeks/months that could be.
"After recent scans the scans showed that he's got some damage especially on one of the ligaments in the ankle," Arteta said at his pre-game press conference.
"I don't want to [give a timeline] because I am not a doctor but it is something quite significant so we are going to lose him for a while. Hopefully not months. Let's see.
"He's our captain. He's been one of the biggest and best players in our team. Our identity is very linked to how he plays and behaves. It's a big test for the team to see how able we are to show a different face."
Even though Arteta refused to put a timeline on his recovery, the former Real Madrid starlet will certainly be out for a number of weeks, ruling him out of fixtures with Manchester City, Paris Saint-Germain and potentially Liverpool between now and the end of October.
Odegaard joins Takehiro Tomiyasu (knee), Oleksandr Zinchenko (calf), Kieran Tierney (hamstring) and Mikel Merino (shoulder) in the medical bay, but Arteta confirmed that Riccardo Calafiori and Bukayo Saka are both available for Thursday.
How do Arsenal replace injured Odegaard?
It was a case of when rather than if Arteta would finally confirm the news that no Arsenal fan wanted to hear regarding Odegaard, who is arguably in the irreplaceable bracket for his manager.
Had the Norwegian suffered this injury last season, Fabio Vieira and Emile Smith Rowe would be ready to carry the playmaking burden, but the duo have since gone to Porto on loan and Fulham permanently respectively.
While none of Arteta's alternative options can fill the Odegaard role with the exceptional close control and panache that he displays, the Arsenal boss at least has several versatile options who can deputise to a degree.
Leandro Trossard was tasked with stepping into Odegaard's boots against Tottenham, but Kai Havertz, teenage sensation Ethan Nwaneri and Chelsea loanee Raheem Sterling can also play just off the striker.