The 32-year-old, who joined Sunderland until the end of the season on March 9, has yet to play for the club and has not featured for his country since 2013 after he lost his place to Paris St Germain's Serge Aurier.
Sunderland also said Eboue did not make the club aware of the matter and had given the former Arsenal player two weeks to appeal the decision.
FIFA said the Ivorian's ban would be lifted if he paid the outstanding amount to the agent, who was named as Sebastien Boisseau.
Eboue was ordered to pay the undisclosed amount by FIFA's Players' Status Committee in July 2013, a decision taken on the basis of the players' agents rules which were in force at the time.
Eboue was fined 30,000 Swiss francs ($31,162) in September 2014 for failing to comply with the decision and given four months to settle the debut, FIFA said.
($1 = 0.9627 Swiss francs)
(Writing by Brian Homewood in Berne and Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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