Following the incident on the Paris Metro European football's governing body UEFA condemned the fans' behaviour, but said that because it had occurred outside the stadium, it was not within its jurisdiction to act upon it.
"UEFA condemns all forms of discrimination and we are appalled by the incident which took place in the Paris Metro on Tuesday," the organisation said in a statement.
"However, as it occurred away from the stadium, it is outside UEFA's remit to act. It is a matter for the local authorities to investigate further and UEFA supports any action that is taken."
Sepp Blatter, president of world governing body FIFA, also expressed disgust over what had happened.
"I also condemn the actions of a small group of Chelsea fans in Paris," he wrote on Twitter. "There is no place for racism in football!"
Chelsea fanzine editor David Johnstone expressed fears for the club's reputation in light of the incident.
"I think the majority of Chelsea supporters are disgusted by what's happened," he told BBC radio.
"The 2,000 who were in Paris today (Tuesday) support a Jewish-owned football team where the majority of players are black and foreign."