Fecafoot said in a statement late Monday that it had instructed its own ethics committee to open an investigation into accusations by convicted fixer Wilson Raj Perumal that there were "seven bad apples" on the West African team at the World Cup.
Fecafoot said it had not been contacted by FIFA when it announced its investigation.
"Yes I have been told about this but let them do their work on this investigation," FIFA President Sepp Blatter told reporters Tuesday in Brazil.
The world body should normally take the lead in investigating allegations of fixing in World Cup matches.
Cameroon was eliminated after losing all three of its group-stage matches at the World Cup: 1-0 to Mexico, 4-0 to Croatia and 4-1 to host Brazil.
Germany's Der Spiegel alleged that in a chat with the magazine hours ahead of the match Perumal - who is linked to previous fixing in African football - correctly predicted the score of the Croatia game and that Cameroon would have a player sent off in the first half.
"Recent allegations of fraud around Cameroon's three 2014 FIFA World Cup preliminary games, especially Cameroon vs. Croatia, as well as the 'existence of seven bad apples (in our national team)' do not reflect the values and principles promoted by our administration in line with the FIFA Code of Conduct and the ethics of our nation," Fecafoot said in the statement, which was signed by interim president Joseph Owona.
"We wish to inform the general public that, though not contacted by FIFA in regards to this affair, our administration has already instructed its ethics committee to further investigate these accusations."
On Tuesday, FIFA spokeswoman Delia Fischer said the governing body would not comment on details "so as to not compromise any possible investigations."
Perumal allegedly predicted the outcome of Cameroon-Croatia in a Facebook conversation with Der Spiegel before the Group A game in Manaus on June 18. The magazine said Perumal, a Singaporean with ties to Asian and Eastern European gambling syndicates, accurately predicted the 4-0 scoreline and that Cameroon would have a player sent off in the first half.
Cameroon midfielder Alex Song, who plays for Barcelona, was sent off before halftime for needlessly elbowing Croatia striker Mario Mandzukic in the back.
Perumal did not give a source for his allegations. In the chat, he also referred to there being "seven bad apples" on the Cameroon team, Der Spiegel said.
That game was the low point of a disastrous World Cup for Cameroon, which conceded nine goals and scored just one in its three games. Cameroon's embarrassing campaign also involved its players threatening to strike before the tournament over bonus payments and an on-field fight between teammates in that Croatia game. In the final minutes of the match, an argument between defender Benoit Assou-Ekotto and midfielder Benjamin Moukandjo ended with Assou-Ekotto head-butting Moukandjo.
Fecafoot had already launched a disciplinary investigation into the behavior of its players in the Croatia game.
"We are strongly committed to employ all means necessary to resolve this disruptive matter," the federation said of the match-fixing allegations.
Perumal was jailed in Finland for match-fixing and is currently in Hungary, where he testified last week in a match-fixing trial.
He is also believed to be behind fixed games involving South Africa's national team in the buildup to the last World Cup, when corrupt referees are thought to have manipulated games.