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Saka will miss Friday's league game against Ipswich Town at the Emirates, along with several others, but Arteta is hopeful the 23-year-old will return to fitness before the season concludes.
Saka has recorded five goals and 10 assists in the league this season, helping Arsenal to third place in the standings. He was forced off in the 22nd minute of their match against Crystal Palace and later left the stadium on crutches.
In October and November, the England international missed three Nations League games as well as Arsenal's league defeat at Bournemouth, and their Champions League win over Shakhtar Donetsk due to injury to the same leg.
"I'm not sure if it's exactly the same (type)," Arteta told reporters on Monday.
"It is in the same leg. He had the third minor injury - I don’t know how big this is going to be. But he already had two."
"It’s not looking good. He's going to be out for many weeks... It could have been much worse. It could have been something else that can take you out for a year."
When asked how he plans to replace Saka, Arteta said: "I'm putting some ideas together but I haven't got there yet."
"Gabriel (Jesus) and Ethan (Nwaneri) have played there, (Leandro) Trossard can play there in relation to how that unit moves. Kai (Havertz) could play there. We will see, try different things and ask how they feel about it."
Arteta also confirmed winger Raheem Sterling has injured his knee and is also going to be out for many weeks.