The Integrity department of the Spanish FA has referred this case to the FA's competition committee, the RFEF told ESPN FC. Proceedings were opened on Wednesday.
The Spanish Players' Union (AFE) issued a statement on Tuesday regarding the incident during Sunday's game, saying: "In any rule of law, the presumption of innocence is a fundamental right of any person until proven guilty. AFE will condemn, as it has always done, any racist or xenophobic action that attacks, both on and off the field, any footballer."
- Marcotti: La Liga miss chance to act over racism
Valencia's players walked off the field as a sign of protest after Diakhaby said he was racially insulted, but eventually returned.
Referee David Medie Jimenez wrote in his match report that after the confrontation between the players, Diakhaby said to him the racist words that Cala had told him but that they were not heard by anyone among the officiating crew.
On Tuesday, La Liga said it is still gathering evidence.
Cala defended himself in a news conference on Tuesday and said: "I'm being accused of being something that I am not. I'm in shock. I'm being judged without people hearing my version of events. No one deserves this.... All that has happened is a circus."
Earlier in the day, Diakhaby spoke for the first time since the alleged incident. In a video posted on social media, the French player said: "On Sunday, in Cadiz, a player insulted me and the words were 'piece of s--- black [man]'. The player said that to me and that is unacceptable...You've all seen my reactions. That cannot happen in life and especially in football, which is a game of respect.
"After that, my teammates and I decided to walk to the changing room, which was the right decision. Then one of their [Cadiz] players came and asked one of our players that if [Juan] Cala apologised, would we be willing to go back onto the pitch, and my teammates and I said 'no', that things don't work like that, that you can't let things like that go by."
Diakhaby said the incident "hurt him a lot" and called for La Liga to take action.
Valencia said the squad ultimately returned to the pitch to play because the referee warned of a possible points deduction if they didn't resume the game.
Cala claims Diakhaby did not hear him correctly.
"I don't know why he is saying that, if he has invented it or misheard what I said," he said. "There are two victims here, him and me. We are both professional.
"I have no problem in sitting with him [Diakhaby] in a room and talking to him. I can tell him what I said and he can tell me what he thought he heard.
"But you cannot accuse someone if you don't have any proof.
"There are seven or eight players around me when he claims I said what I said and no one heard anything. There are no fans at the stadium and there are plenty of microphones, so everything can be heard.
"There is no racism in Spanish football. There are many black players in Spanish teams, they are all integrated."
Cala said he will take legal action against anyone that has put his honour in doubt.
Valencia, meanwhile, said in a statement that Cala has missed an opportunity to apologise to Diakhaby.
The statement said: "Juan Cala has lost a great opportunity to accept that mistake and apologize to the person affected. Instead, he has attacked the player himself and other members of Valencia CF.
"Valencia CF totally believe in their footballer and reiterate their full support to him. After the threats made by Cala in his news conference on Tuesday, April 6, the club, its president Anil Murthy and player Mouctar Diakhaby keep intact their deep conviction to fight wherever necessary and until the end for the good of soccer.
"Valencia CF will not stop fighting for the improvement of regulations and the fight against racism in football and in society."