The FA said the 33-year-old Spaniard, who joined Leeds from Real Madrid last year, must also attend face-to-face education after the breach of rule E3 (2) which covers discriminatory abuse.
Casilla had denied using racially abusive or insulting words. Media reports said the incident involved Charlton forward Jonathan Leko, who was born in the Democratic Republic of the Congo but has represented England at various age group levels.
The Spaniard said in a statement on social media that he was "sad and devastated" at being accused and believed firmly that racism should not be tolerated in any walk of life.
"I do not feel at all that the guilty verdict is a clear reflection of the incident," he said.