There were fears the talented player would face a long time on the sidelines as he would need surgery over the thigh injury he sustained in the opening day defeat at Chelsea.
Ayew, who joined the Hammers from Swansea was taken off in the 35th minute of their clash with the Blues while attempting to track back.
The West Ham record signing of £20.5m, who joined the club earlier this month, was feared to be facing up to four months if surgery was required.
But the club’s head of medical and sports science Stijn Vandenbroucke says the Ghana international will not require surgery and he could return to the pitch earlier than expected.
“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 timeline on the rehab, but we are positive to reintroduce him in December.”