Jesus had the surgery on Wednesday after experiencing discomfort in the same area that was operated on when he suffered a serious knee injury at the World Cup last year.
Jesus spent three months on the sidelines before recovering in time for the final weeks of Arsenal's failed bid to win the Premier League.
Having been absent for Wednesday's Emirates Cup friendly against Monaco, Jesus will miss the start of the new season, including Sunday's Community Shield clash with English champions Manchester City.
But Gunners boss Arteta is hopeful Jesus will play a major part in his side's title challenge.
"He's obviously disappointed because he was feeling good and then this issue came up that nobody expected," Arteta told reporters on Friday.
"We had to do a little procedure there but unfortunately it was the best thing to do and the quicker the better. We made that decision. I'm sure he will be back soon and very fit."
Bukayo Saka was an unused substitute against Monaco due to illness, but Arteta confirmed the England forward is "much better" and should be ready to face City at Wembley.
All of Arsenal's close-season signings are in contention to start on Sunday, with Jurrien Timber, Declan Rice and Kai Havertz aiming to make an early impact.
Rice was also a target for City before joining Arsenal from West Ham, providing Arteta with proof his club can compete with Pep Guardiola's men on and off the pitch.
"The important thing now is that when we have a target that we have the resources that we need to bring that player in," he said.
"But as well that we can convince him and what we tell him excites him, that he feels inspired and he wants to be part of it. That is the feeling we are getting with every player I want to sign."
Arsenal finished five points behind City after squandering the eight-point lead they held at the start of April.
It was a bitter blow for fans who had dreamt of Arsenal winning their first title since 2004.
Arteta hopes Rice can make the difference this time as Arsenal look to end City's three-year reign as champions.
"His leadership skill is unquestionable and when you meet him and spend five minutes with him," he said.
"You already get the feeling and impression that he will help so much, the dressing room and approach that we want to take in games."
