Spain's Football League followed suit and warned of sanctions for racist behaviour, while announcing compulsory training for all its member clubs to avoid a repeat of the same behaviour.
Only a week after a fan threw a banana at Barcelona's Brazilian defender Dani Alves, another player, Levante's Senegalese midfielder Papakouli ('Pape') Diop, was subjected to monkey taunts on Sunday.
"Uefa and its president Michel Platini strongly condemn all forms of discrimination including recent racist behaviour of fans in Spain," Platini's spokesman Pedro Pinto said in a message on Twitter.
"Uefa has tough rules and sanctions against all forms of discrimination for all of its competitions," he added.
"Where instances occur outside of our jurisdiction, we support appropriate action being taken by the relevant authorities."
The 28-year-old Diop accused Atlético Madrid fans of subjecting him to monkey-chanting abuse as his side inflicted a shock 2-0 defeat on the Liga leaders at the weekend.
He reacted by dancing in front of the travelling fans at the final whistle, and television images showed some furious Atlético supporters making monkey gestures.
"It affected me a lot," Diop said.
"I don't have anything against the Atlético fans. It is a provocation I get in many grounds. It has to stop. I don't know if it is racism or a lack of respect," he added.
"They have to stop making monkey gestures at black players."
Spain's professional football league, the LFP, said it "strongly condemns" any racist, discriminatory, violent, xenophobic or intolerant acts, especially in football and sport.
The league warned of sanctions for serious breaches of anti-racism laws and said all member clubs would be obliged to follow special training to prevent a repeat of such behaviour.
"The LFP will pursue this type of behaviour," it said in a statement.
The monkey slurs made headlines in the British press.
"Spanish football must face up to the fact that they have a serious racist problem. They can't continue to bury their heads in the sand," tweeted former England international Gary Lineker who once played for Barcelona.
A week earlier, Barcelona's Brazilian international Alves shone a spotlight on racism in Spanish football when he took a bite out of a banana thrown at him during his side's win over Villarreal.
Star players of different nationalities and races including Neymar, Sergio Aguero and Luis Suarez joined a "we are all monkeys" campaign after the incident.
The alleged banana-thrower was subsequently arrested and handed a lifetime ban from the stadium by Villarreal.
Alves said it was not a one-off. "I have been in Spain 11 years and it has been the same for 11 years. You have to laugh at these backward people," he said after the game.
Serious racist problem
Top-selling Spanish sports daily Marca said a delegation of Atlético players visited Diop in the changing rooms after the match to offer their apologies. But there was no official public reaction from the club.
"Diop's little dance directed at the Atlético fans was over the top," Barcelona-based sports daily Mundo Deportivo said Monday. "But the alleged racist shouts were, too ... just like any other insult," it added.
The reaction echoed the tone of some comments by Spanish football officials after the Alves banana-throwing scandal a week earlier.
"It is not everyone. I want to think these are isolated incidents. In football there is no racism, not at all," Spain coach Vicente Del Bosque said at the time.
Salvador Rodriguez Moya, journalist and author of "Black card to racism" which recounts 300 racist acts in Spanish football, said it would be wrong to condemn all of Spain and all Spanish football as racist, describing the incidents as isolated and anecdotal.
"But it is still true that it is like a sleeping volcano, which could erupt at any moment," Moya said in an interview.