Saka, who scored the opening goal of Arsenal's 3-1 win over Liverpool on Sunday, was forced off about 10 minutes from injury after receiving treatment on his right foot and ankle on the pitch.
Rather than go down the tunnel, Saka sat with his team-mates on the bench to watch the rest of the match and was able to walk onto the pitch to celebrate at the full-time whistle.
Speaking to reporters after the game, Arteta said of Saka: "He should be fine, I think. He got a kick I think on the ankle or on the back of his foot, but he should be fine."
Jesus was absent from the matchday day and Arteta confirmed before the game that the striker had suffered a knock in training, telling Sky Sports: "Unfortunately, he had a setback in training and he wasn't fit to play. It's something related to his knee, but I think it's a short-term thing."
Elaborating after the game, Arteta said: "With Gabi we expect it to be some days [off]."
Zinchenko was forced off at half-time, to be replaced by Jakub Kiwior. Arteta said of the defender: "With Alex we don’t know. He felt something in his calf again so we had to take him off."