"The scan showed there is a muscle injury," Arteta told reporters on Friday.
"We might lose him for a few weeks. With Gabi, I cannot give you any time frame because he always surprises us."
"It's what we want to avoid but with the schedule that we have and the amount of games that we have, it's something that we knew was going to happen," Arteta said.
"It's happening to every club in the Premier League so there's no difference."
Jesus was forced off with a hamstring issue after scoring a goal and assisting another in Arsenal's 2-1 Champions League victory in Spain on Tuesday that took them top of Group B.
Midfielder Thomas Partey has also been ruled out for a couple of weeks due to a muscle injury.
"What we need is more players," Arteta said.
"There's no secret, the players have a certain
amount of energy and the battery only lasts so long or we will burn them out."
Arsenal sit third in the Premier League, just two points behind leaders Tottenham and level on points with Manchester City. Sheffield United are last with just a point after nine games.
Arteta said his team will not take Sheffield United lightly, especially as they played well in a 2-1 loss to Manchester United last time out.
"The way they have played against all the other teams has been strong, they're clung on and then it's been late goals conceded," the Spaniard said.
"They are fighting for their lives so it will be a tricky game.
"Everyone is on their toes, they know what is coming and I was very clear with them."
