The 17-year-old was carried off during Saturday's game against Lille.
Ayew, who has played six matches in Ligue One so far this season, suffered the setback on his ankle.
Despite the seemingly serious injury, the youngster says he has seen some improvement in the past 48 hours.
He is keen to return to action at the weekend when Marseille face Monaco on Saturday.
"I am happy to report that the ankle has improved in the past 48 hours," Ayew said.
"I am confident that by Saturday when we play Monaco I should be ready for action."
Ayew is the son of Ghana legend Abedi Pele who also played for Marseille in the 1990s.