The 26-year-old has been granted an extended holiday after Chile’s victorious Copa America campaign and will not return to training until August 3
The Gunners’ league season begins at home to West Ham on August 9 – seven days after they face Chelsea in the Community Shield at Wembley.
Sanchez helped guide Chile to victory in the Copa America earlier this summer and his extended holiday means that he has not travelled with the rest of Arsenal’s squad for their pre-season tour of the Far East.
“He’ll be back with us on August 3 and it takes about three weeks to get competitive,” said Wenger.
“It could take him a little bit less time [to get match fit] but he’ll miss our first game.”
Danny Welbeck has also been ruled out the Barclays Asia Trophy which begins against a Singapore Select XI on Wednesday, but Wenger expects the striker to recover from his knee injury before the end of July.
“Danny’s injury is a minor one but it look much longer to settle than we expected. But he will be part of the Emirates Cup pre-season tournament,” the Arsenal manager added.