Adebayor picked up a groin problem during Arsenal’s pre-seasour training camp in Austria.
Gunners chief Arsene Wenger told the club’s website: “Adebayor has a groin problem.
“He missed the Emirates Cup and will miss the Ajax Tournament.
“At best he will be back next week. We hope he can come back in to normal training on Tuesday and Wednesday.
“But I think he will miss the start of the Premiership.”