Mikel Arteta targets more silverware after extending his Arsenal contract until 2030
The defender was carried off the pitch on the back of Illan Meslier, with those amateurish images leaving Arteta unimpressed.
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.
"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.
"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."
In the absence of Zubimendi and Hincapie on Tuesday night, Arsenal beat Lille 3-0 to make it 14 straight wins in the league phase of the Champions League.
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.
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"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."