The Marseille forward, who has scored penalties in two of his nation's five Group E matches to date, was substituted in the second half of Ghana's 1-0 defeat to Uganda on Saturday.
And Ayew will not recover in time to face Togo in Tamale, as managerless Ghana go in search of a point that will guarantee their qualification for next year's finals.
The Ghana Football Association (GFA) confirmed Ayew's absence on Monday after the 24-year-old had undergone tests.
Team doctor Baba Adam is quoted as telling Africanfootball.com: "On the pitch we examined Dede [Andre] and our immediate observation was that it was a soft tissue contusion - a contusion of the upper part of the inner thigh.
"When we arrived in Ghana we sent him for an MRI investigation and it revealed that he had a minimal tear.
"The thigh has been sore and we advised that he should stay, intensify the physiotherapy on him and all things being equal in two to three weeks he should be up and about."
Ghana, who will also be without Kwadwo Asamoah (knee) and Asamoah Gyan (thigh), sit top of Group E with eight points heading into Wednesday's final round of fixtures, but all four teams in the group can still secure a top-two finish and automatic progression.
Togo are two points behind the leaders in fourth and need to win in Tamale, while Guinea and Uganda - who meet in Casablanca - are second and third respectively with seven points.
Both Ghana and Togo had the opportunity to qualify with a game to spare, but the former went down to Uganda and Togo were beaten 4-1 by Guinea.
Alban Sabah could make his first start for Togo after the former German youth international was granted permission to switch allegiance prior to the meeting with Guinea.
Sabah was an unused substitute for that game, while Mathieu Dossevi - who has also committed his international future to the West African nation after previously representing France at youth level - played the first half and will hope to feature again.
