Rice and Saka injuries add to Arsenal's mounting worries
Rice went off after 71 minutes and Saka was replaced 10 minutes later with both sustaining knocks.
"It doesn't look good because for two players of that importance to say they want to come off is unusual," Arteta told reporters after the London derby at Stamford Bridge.
"I don't expect them to be fit (for the international break) because if not they don't come off."
Arsenal, who began without the likes of Riccardo Calafiori and Takehiro Tomiyasu, took the lead with a Gabriel Martinelli goal but were pegged back when Pedro Neto was allowed far too much time and space to drill in Chelsea's equaliser.
The result left Chelsea in third place and Arsenal fourth - both of them nine points behind leaders Liverpool.
Arteta said he was disappointed with the way his side conceded the equaliser after working so hard to get ahead.
"After scoring the first goal I'm very disappointed with how we conceded the goal. That's nowhere near the standards," the Spaniard said. "That's not very much like us.
"I think today we have to fault ourselves. That's something that we have to do better."
One positive for Arsenal, who have now gone four games without a win in the Premier League, was the return of captain Martin Odegaard to the starting lineup after a lengthy lay-off with an ankle injury.
"I don't know another player that is capable of doing that after six weeks out," Arteta said of the Norwegian's performance.
While much of the focus surrounds Arsenal's sudden loss of form, Chelsea head into the international break in the top three of the Premier League for the first time since the 2021-22 season when they came third behind Man City and Liverpool.
Tasked with blending a huge and expensively assembled squad, Enzo Maresca has so far done an impressive job.
"It's nice, especially for the fans after the last year has not been great - or at least what this club is used to. For sure, it is something nice," the Italian said.
"The performance was good. The game in some moments was open, anything can happen in both sides. We 100% deserved a point."
