The fire swept through the club's newly expanded youth training center in the early hours of the morning and engulfed the dormitory in flames as the players were sleeping.
It is common for Brazilian clubs to host young players in dormitories while they are training with youth teams or at the club for trials, especially those from poor backgrounds or from outside the city.
Three people were also injured and were taken to a local hospital.
"It's the worst tragedy in the club's 123 years", said Flamengo president Rodolfo Landim, who visited the scene.
The fire brigade said in a statement that the center was "in the process of" meeting fire safety standards but did not yet have a certificate of approval.
Some people had managed to escape the burning building, but the ferocity of the fire prevented firefighters from entering the facility.
The cause of the fire is now unknown.
Brazil's Pele, widely regarded as the best player to ever live, said: "It's a very sad day for Brazilian football".
Officials postponed Saturday's two semifinals of the Guanabara Cup, one of which was between Flamengo and Fluminense at the famous Maracana stadium, host of the 2014 World Cup final.
Jefferson Rodrigues, who runs a small inn near the club, said he had reached a 15-year-old player he had befriended.
Like many clubs who sign youngsters from across the country, the facility has accommodation for teenagers, although it was unclear exactly how many players were among the dead.
Real Madrid star Vinicius Jr came through Flamengo's system and not long ago was living in the training facility. The most important thing now is to dedicate ourselves to trying to minimize the suffering and pain of these families who are certainly suffering a lot and be sure that Flamengo is taking care of it and will spare no effort to minimize this.
Joao Pedro da Cruz, a 16-year-old player in the Flamengo youth league, told the G1 news portal that he decided not to spend the night at the facility because the team wasn't going to train on Friday, and he went to a friend's house instead.
The dream of many youths in Latin America's largest nation, victor of five World Cup titles, is to make it into the ranks of professional soccer. The facility has accommodation for teenage players.
As well as being one of Brazil's most successful football clubs, Flamengo also has basketball, rowing, swimming and volleyball teams.