Belgian Put, who was appointed in March 2018, saw Guinea beaten 3-0 by finalists Algeria in the first knockout round having scraped through as one of four third-place teams in the group stage.
"The coach is dismissed. We're going to talk with him about the terms of his departure. Feguifoot has ended the partnership with Paul Put," said Antonio Souare, the head of Guinea's football federation.
Souare added a return of three wins, four draws and five defeats in 12 matches played under Put was "not satisfactory".
Put, 63, led Burkina Faso to the Cup of Nations final in 2013 before losing 1-0 to Nigeria.