The team was reportedly fined €600 (US$786) for abusing Real Madrid defender Roberto Carlos during last Saturday's Spanish league match.
A federation spokesman said he couldn't confirm the figure but it is the same amount that Albacete Getafe Malaga and Atletico Madrid were fined for racist taunting earlier this season.
Deportivo supporters made monkey noises at Roberto Carlos during the match forcing referee Jose Losantos Omar to stop the match and request that stadium officials ask spectators to stop.
Racist taunting in Spain has also marred international games this season.
FIFA fined the Spanish federation after England's black players were abused during November's friendly in Madrid and Real Madrid and Sevilla were fined by UEFA for incidents at Champions League and UEFA Cup games.
On Tuesday Spain coach Luis Aragones was fined €3000 (US$3940) by the federation for a racist comment about Arsenal striker Thierry Henry and an outburst about Britain's colonial past although he was cleared of racism.