The score was 1-1 when Diakhaby was involved in an altercation with Cadiz's Juan Cala. Valencia's Gabriel Paulista then kicked the ball out of play and the players from both sides walked off the pitch.
Following a short break, the players returned to the pitch, but Diakhaby did not return and Hugo Guillamon came on in his place. Cala had put Cadiz ahead on 14 minutes, before Kevin Gameiro equalised for Valencia five minutes later. Marcos Mauro scored in the 88th to give Cadiz the 2-1 win.
"We offer our complete backing to Mouctar Diakhaby," a tweet posted on Valencia's page read. "The player, who had received a racial insult, requested that his teammates return to the pitch. WE SUPPORT YOU MOUCTAR. NO TO RACISM."
Diakhaby was seen watching the remainder of the first half from the stands.
After the match, Valencia defender Jose Gaya said the team was told to return to the pitch.
"Diakhaby told us he heard a racist insult so we all went off the pitch. We were told that we had to play because if we didn't they would take the three points off us and maybe we'd be docked more points," Gaya told Spanish network Movistar.
"Diakhaby asked us to play on, we wouldn't have done so if he hadn't done so. He said he wasn't in the right state of mind to keep playing. He is devastated."
Referee David Medie Jimenez said in his report that Diakhaby had told him Cala had used a racial slur against him, although Cadiz coach Alvaro Cervera said his player had assured him he had not insulted the Frenchman.
It was the first time a La Liga match had been halted following an accusation of racism. On Monday, La Liga president Javier Tebas said that the league had opened up an investigation.
"Something happened and we will try to clear that up because the league does not permit for racism in our sport. The versions are contradictory but observing the conduct of [Diakhaby] something happened," Tebas told Movistar.
Gaya said he had heard the comment Cala made to Diakhaby.
"It was a very ugly insult which I won't repeat. We haven't been able to speak with Cala because he was the last player to leave the pitch. I'm certain that he said something. It was a very strange game," Gaya said.
Valencia coach Javi Gracia said Diakhaby had been "seriously insulted and was quite shaken."
He added: "Logically we decided to tell the referee we didn't agree with that [playing on] and that we didn't want to continue playing. While we were in the dressing room we were told we could potentially be sanctioned if we didn't return.
"We spoke to Diakhaby, he said he was not able to play but he understood we needed to return to play rather than be sanctioned and so we returned with the intention to fight for the victory."
Gracia added that the match referee and assistants did not know what had been said to Diakhaby. He also did not reveal who had told his team they could be sanctioned.
Cadiz released a statement saying the club was "against any manifestation of racism or xenophobia, regardless of who the perpetrator is" but did not mention Cala.
"We don't doubt the honesty of all members of our squad, who are firm believers in the fight against racism and whose attitude in every game has always been exemplary," it added.
"The club cannot assess incidents in a match between players and we always demand that our players show respect and responsibility towards their opponents."
When asked about the incident on Monday, Real Madrid coach Zinedane Zidane condemned racism of any form in the league.
"What I can say is one clear thing on racism: zero tolerance. I don't know exactly what happened yesterday, I wasn't there, but what I can say is what I feel inside, that's respect towards people first, that's the most important," he told a news conference.
"Zero tolerance for racism... Not just in terms of words, but at every level, all behaviour."