Ayew, who joined West Ham from Swansea for a club record fee of £20.5m earlier this month, was withdrawn 35 minutes into his Hammers’ debut after pulling up with the problem while attempting to track back.
West Ham manager Slaven Bilic admitted last week the Ghana international could be out for up to four months if surgery was required.
But the club’s head of medical and sports science Stijn Vandenbroucke has confirmed Ayew will not require an operation and has already started his rehabilitation programme.
“Andre Ayew suffered a rare but very serious thigh injury at Chelsea, which will take time to recover from,” he told the club’s official website.
“Andre will not have surgery and we have started the rehab straight away, working two times a day.
“Andre is a highly professional athlete with a positive attitude that no doubt will affect the return to play date.
“It is early to put a time-line on the rehab, but we are positive to reintroduce him in December.”