Sakho pulled of the AFCON because of a back problem but then went on to score for West Ham in their 1-0 FA Cup win at Bristol City on January 25.
The Senegal Football Federation lodged a complaint with the FIFA after learning of Sakho's involvement in the contest.
However, the world governing body has opted not to expel the London club from England's most prestigious cup competition or punish Sakho with a suspension.
Instead West Ham have been fined 100,000 Swiss Francs, which works out at approximately £71,000, while Sakho has been issued with a reprimand.
The decision does, however, cost West Ham most of their £90,000 prize money for winning in the fourth round of the FA Cup.
A FIFA statement read: "The FIFA Disciplinary Committee has found the club and the player to have violated art. 5 of Annexe 1 of the Regulations in relation to the match played by Sakho on 25 January 2015.
"The club has been fined CHF 100,000 in accordance with art. 10 c) and art. 15 of the FIFA Disciplinary Code (FDC) and issued with a reprimand, while the player has been sanctioned with a reprimand in accordance with art. 10 b) and art. 14 of the FDC."
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