Hincapie picked up the issue in a training session after Arsenal's win over Leeds on Saturday.
Hincapie was sent for a scan on Monday and the result of that is a spell on the sidelines, as Arteta ruled him out of the upcoming matches.
"Piero is improving but it looks more significant," Arteta said.
"I think it will be a matter of weeks but we don't know exactly how many."
Zubimendi also suffered an ankle injury in that same session, though his situation is "much, much better".
The Spaniard missed the Champions League clash with Lille on Tuesday night but he is not expected to be out for an extended period.
Arteta indicated that Zubimendi is likely to only be out for a matter of days, which could leave him in line to return against Nottingham Forest on Sunday.
"Zubi I expect, yeah [only days]," Arteta said.
"We have to see the moment he goes on that pitch, how he deals with the pain and some small feelings that he will have."
Saka scored and assisted in his cameo, responding to Arteta's challenge a day earlier to score "two or three goals per game".
"After the press conference, he was on the massage table and I said, 'Bukayo, I just killed you in the press conference, good luck tomorrow," Arteta joked.
"He was laughing, he knows that we have discussed these kind of things. He takes it because he wants to be the best version of himself. In order to do that, you have to put big objectives challenges and try to reach them by working and being consistent.
"When it doesn't work, keep going because he has the ability to do it."
Arteta also revealed that Saka's performance came despite the winger having been ill in the build-up to the match.
"He wasn't feeling that good yesterday and today, because he had a sort of illness," Arteta said.
"He wasn't ready to start but he was really keen to contribute to the team if it was needed. He came on, he made a huge impact and delivered with real quality."