The world governing body's disciplinary committee overturned the result after ruling that Gabon defender Charly Moussono was not eligible to play because he had previously represented Cameroon.
FIFA's own statistics showed Moussono had represented Cameroon in the 2006 Beach World Cup in Brazil.
The decision means that Gabon have dropped to third in African qualifying Group E with three points from two games, the same as Niger and one behind new leaders Congo.
Burkina Faso, with one point, are the other team in the group.
Moussono, 28, played for Gabon when they co-hosted this year's African Nations Cup with Equatorial Guinea and started in all four of their matches.
The Confederation of African Football (CAF), which organises the Nations Cup, was not immedately available for comment. Gabon reached the quarter-finals, surprisingly qualifying at the expense of Morocco.