The 19-year-old has also been warned about his future conduct.
Suso last month posted a photo of Enrique having his teeth whitened with the comment: "What f*** is he doing? This guy is gay... he does everything except play football."
The attacking midfielder later deleted the tweet and uploaded the photo with a different comment, saying: "I dunno what to say..."
Suso has now been reprimanded for the remark.
The FA said in a statement: "Following an independent regulatory commission hearing yesterday (Monday, December 17 2012), Liverpool's Jesus Fernandez Saez (Suso) has been fined £10,000 and warned as to his future conduct for a comment posted on Twitter.
"The charge, which the player admitted and requested a paper hearing, was that he acted in a way which was improper and/or brought the game into disrepute in that the comment was posted on his Twitter account and included a reference to a person/s sexual orientation and/or disability."
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Source: PA