The 28-year-old Chile international has an abdominal strain that could also keep him on the sidelines for the trip to Stoke on August 19.
The Gunners forward has been heavily linked with a move away from the London club this summer.
“Sanchez will not be available. He had a little abdominal strain that he caught on Sunday morning in training. He had the scan two days ago. He’s out for, er, a while,” Arsenal head coach Wenger told reporters.
“I don’t know if it will be two weeks or one more week but I don’t think he will play at Stoke. Sanchez is always loss but we have all the other players prepared and they are ready.”