Saka, 25, suffered the injury 10 minutes into Arsenal’s 2-2 Champions League draw at Bayern Munich on Wednesday and was forced off the pitch.
"He's going for an MRI this afternoon because he had a lot of fluid in the area, so it was difficult to understand the severity of the injury. We will know tomorrow," Arteta told a press conference.
"We need a few more scans and opinions from the specialists. When a player is struggling to walk off the pitch, and he's restricted in his movement, they are not good signs."
Following the England international's setback, Arteta also highlighted the strain the congested schedule places on players, calling for greater consideration from the governing bodies.
"If they can support the amount we are putting into these players, it would be really appreciated," he said.
"We have to play three times in less than six days; the games are so demanding, we are chasing until the last minute."
After facing Everton, Arsenal will visit fourth-tier Fleetwood Town in the EFL Cup fourth round on Tuesday.