The 20-year-old was substituted at half time on Monday after being involved in a clash with Crystal Palace's James McArthur, and that was only the third time this season that Saka has played fewer than 60 minutes for the Gunners in the Premier League.
Mikel Arteta was not pleased with the challenge from McArthur and after the match he suggested that the Eagles midfielder should have seen a red card for the tackle.
However, The Sun reports that Arteta is confident that the England international will make a full recovery in time to feature for the Gunners later this week, after initially fearing that the injury could set him back until after next month's international break.
Saka made 32 Premier League appearances last season, and having played his part in each of Arsenal's eight opening fixtures so far, the youngster is proving to be a regular figure in the Gunners' lineup.
The winger has one league goal and one league assist to his name so far this campaign, which both came in Arsenal's North London-derby victory against Tottenham Hotspur last month.