Patrick Vieira took City's Under-21 side off the pitch during the preseason clash with NHK Rijeka 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 Rijeka 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 has confirmed it is 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 has previously denied any wrongdoing insisted that the allegations from City are "unfounded".
"We strongly reject unfounded racism allegations mentioned in the statement Manchester City has posted on its website and want to stress that Rijeka itself had six players from Nigeria on the team," Rijeka said in a statement issued on Wednesday.
"We also want to point out that HNK Rijeka, in cooperation with FARE (Football Against Racism in Europe), has been supporting the campaign against racism for years and we strongly condemn every such incident."