Patrick Vieira took City's Under-21 side off the pitch during the pre-season clash with NHK Rikeja on Tuesday, after an opposing player was alleged to have racially abused 19-year-old French midfielder Fofana.
Fofana had been sent off for kicking out a Rikeja played late in the first half and it is alleged that he was reacting to being taunted.
City's management staff decided the game should be cut short, then called for the CFF to investigate - and the governing body have confirmed are looking into the incident.
A CFF statement said: "[The] Croatian Football Federation is in a process of gathering information regarding the alleged incident and if there are any decisions to be made we'll make it public on our website.
"CFF follows a strong 'no racism' policy so we take all accusations of racism very seriously. [The] Fight against racism [and any sort of discrimination] is one of key components of our president Davor Suker's programme and that is why we will have a good look into this matter."
Rikeja denied any wrongdoing in a statement on the club's official website.
"Rijeka clearly and unequivocally rejects any possibility that the players at the match against Manchester City participated in assaulting the rival players on racial, religious or ethnic grounds," said the club.
"We want to point out the fact that we mentioned at the game we had six players from the Nigeria squad, players who live and train together with our other players, who learned the Croatian language and who have never experienced any discomfort by team-mates - as they themselves can attest.
"We also want to point out that Rijeka, in co-operation with FARE (Football Against Racism in Europe), supports a campaign against racism and strongly condemns any incident of its kind.
"Because of this, we are surprised by the unpleasantly harsh and baseless accusations of which we are accused and that we completely reject."
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