The 25-year-old is an important player for Japan, for whom he has earned 37 senior international caps to date.
Japan are in Group D for the 24-team tournament, which was originally due to be held in China last summer.
However, they relinquished hosting rights in May 2022 amid continued Covid-19 challenges and Qatar was later selected over rivals South Korea and Indonesia once the bidding process was reopened, with the competition then moved to a new early 2024 slot due to the extreme summer heat in the country.
Japan's first game comes against Vietnam in Doha on January 14, with subsequent group matches against Iraq and Indonesia.
Tomiyasu's injury may now place his Asian Cup participation in some doubt, though he would surely likely still be selected for the tournament even if he was not fit to start the campaign.
If four-time winners Japan, who lost the 2019 showpiece to 2022 World Cup hosts Qatar in Abu Dhabi, were to reach the final of the tournament for the sixth time, then Arsenal would be without the valued full-back until after February 10.
Being without Tomiyasu for any period of time is a blow for Arteta, with the defender having proven one of the title-challenging Gunners' best performers over recent weeks and earned player of the month honours at the Emirates Stadium for October.
Tomiyasu limped off in the closing stages against Wolves and then missed Tuesday night's dramatic 4-3 win at Luton, with Arteta revealing a downbeat update on his condition after that chaotic game at Kenilworth Road that saw them open up a five-point lead at the top-flight summit.
"We had a scan and it’s not good news," the Spaniard said. "He’s got an injury in his calf and he’s going to be out for a while."
Tomiyasu's absence leaves Arsenal a little light on full-back options, with summer signing Jurrien Timber also sidelined with a serious knee injury suffered on his Premier League debut back in August.
Arsenal face a potentially tricky reunion with former boss Unai Emery and high-flying Aston Villa this weekend, before they conclude their impressive Champions League group stage campaign away at PSV Eindhoven and also play Brighton, Liverpool, West Ham and Fulham before the end of the calendar year.
Liverpool are the visitors again in early February, a busy month that also includes contests against West Ham, Burnley and Newcastle plus a round-of-16 tie in the Champions League.
In addition to Tomiyasu and Timber, Arsenal are also without midfield trio Thomas Partey, Emile Smith Rowe and Fabio Vieira at present due to injury.