The world game's governing body has decided on the sanction after Minyahile Teshome Beyene played in the fixture on June 8, which Ethiopia won 2-1, despite being suspended after collecting two yellow cards in previous fixtures.
FIFA has awarded Botswana a 3-0 win, throwing Group A wide open once again.
Ethiopia thought they had opened up an unassailable five-point gap at the top but their punishment means they are now only two ahead of second-placed South Africa with one game to go. Botswana are third on seven points, one fewer than South Africa.
Ethiopia, who were also fined 6,000 Swiss Francs (£4,163), visit the Central African Republic in September while Bafana Bafana host Botswana.
The 10 group winners advance to five play-off matches with the victorious nations taking their places in Brazil next summer.