The Spanish side, managed by former Watford boss Javi Gracia, left the field partway through the first half in the aftermath of a confrontation between defender Mouctar Diakhaby and the home side’s Juan Cala.
But what actually happened, and what has been the response to the incident?
Why did Valencia walk off?
Valencia left the field against Cadiz shortly after the 30th minute, with the score tied at 1-1.
The home side had taken an early lead through Juan Cala, before Kevin Gameiro equalised for the hosts in the 19th minute.
Not long after that, Cadiz fired a free kick into the box, at which point Cala collided with Valencia defender Mouctar Diakhaby.
The two players exchanged words, after which the centre-back reacted angrily to something said by the 31-year-old forward.
While play continued, Diakhaby followed Cala to the half-way line, and had to be held back by teammate Gameiro and Cadiz’s Fali.
The 24-year-old was visibly shaken by the incident, and was initially shown a yellow card for unsportsmanlike behaviour.
Diakhaby then entered into a lengthy conversation with the referee to explain the reason for his anger towards Cala, before he and his teammates walked off the pitch in an act of solidarity against the alleged abuse.
What happened after Valencia walked off?
It initially appeared that the game would have to be called off, with Valencia refusing to return to the field of play.
Gracia’s men subsequently held a meeting in the dressing room, however, and after a 20 minute delay, decided to finish the game.
Diakhaby was substituted during the break in play, and was replaced by Hugo Guillamon.
Cala stayed on the pitch until half-time, at which point he was taken off.
Cadiz went on to win the game 2-1.
What has the response been to the incident?
In the immediate aftermath of the incident, Valencia sent a tweet from their official Twitter account that read: “No To Racism”, before adding that the players would return to the pitch "in order to fight for the honour of the club, but denounce racism of any kind".
Following on from that tweet, the club added: "The player, who had received a racial insult, requested that his teammates return to the pitch. WE SUPPORT YOU MOUCTAR. NO TO RACISM."
Speaking after the match, Valencia captain Jose Gaya said: "Diakhaby mentioned to us there were some insults from the opposition, and we are not going to accept that.
"We decided to leave the pitch and were just waiting to see what was going to happen.
"We were going to stay with our team-mate but we were told we would have to leave the pitch, we came back on the pitch because we were told we were probably going to lose the game.
"That's what happened and Diakhaby asked us to return as well and that's why we decided to come back.
"He told us to continue but he didn't want to - he's not happy after the game, he's quite upset and very hurt."
Cadiz confirmed that Cala will address the media with regards to the incident on Tuesday.