The Black Stars lost their third place play-off match against Burkina Faso 1-0, marking the end of the Israeli as the coach of the Ghanaians.
The result leaves the Israeli short of his given target - to win this tournament.
Grant's two-year contract will not be renewed and the search is on for a successor, senior Ghana Football Association officials have revealed.
The former Chelsea manager took over as Ghana coach one month before the last Nations Cup in Equatorial Guinea and took the side to the final where they lost to Ivory Coast on penalties.
At the tournament in Gabon, Ghana reached the semi-finals but were beaten 2-0 by Cameroon in Port Gentil on Thursday.
Israeli Grant avoided questions about his future, saying now was not the time to talk it.
Ghana made a poor start to their World Cup qualifying group with a single point from two games.
They have now qualified for six successive Nations Cup semi-finals but their last victory in the tournament came 35-years-ago.