The victims have not been named but are said to include young players staying at Ninho de Urubu, the training ground of Flamengo football club in Rio de Janeiro.
Three teenagers were also injured, one of them seriously.
The cause of the blaze is being investigated.
However, one young player said the fire started in an air conditioner in his room.
“The air conditioner caught fire, and I ran out,” said Felipe Cardoso, a player with the under-17 side. “Thank God I managed to run and I’m still alive.”
Flamengo is one of Brazil’s biggest and best-known clubs internationally. They currently sit at second place in Brazil’s Série A table and have won the league five times.
Brazil football legend Pelé described the club as “a place where young people pursue their dreams”.
“It’s a very sad day for Brazilian football,” he tweeted.
Former Brazil star Ronaldinho offered his condolences for the “terrible tragedy” in a tweet on Friday morning. He published the club’s crest in black-and-white alongside the message.
What do we know so far?
According to the G1 news portal, the fire began at 05:10 (07:10 GMT) and was extinguished by 07:30.
None of the victims has been identified but the youth players are said to be aged between 14 and 16. One of the three injured, a 15-year-old boy, suffered severe burns and was transferred to a specialist hospital, reports said.
The area has been hit by severe storms and heavy rain in recent days and the weather may have left the facility without water or electricity when the fire struck, G1 reported.
Flamengo’s pride in youth academy
Analysis by Fernando Duarte, BBC Brasil
Flamengo is one of the few Brazilian clubs that can boast an expressive national fan base in Brazil. A poll released last April suggested they are the first team for 32.5 million Brazilians.
The club owes a great chunk of this support to an incredible run of four Brazilian titles and a victorious Copa Libertadores campaign (the South American version of the Uefa Champions League) in the 1980s.
It has also produced arguably one of the greatest all-time Brazilian players – Arthur Antunes “Zico” Coimbra, a member of the 1982 World Cup squad that failed to win the titles but won worldwide plaudits for its slick style.
The club is also proud of the traditional of its youth academy – their motto is “we make our star players at home – which will make this tragedy even sadder.
Who are Flamengo?
The club’s most prominent former players include World Cup winners Ronaldinho, Bebeto and Romario.
As well as being one of Brazil’s most successful football clubs, Flamengo also has basketball, rowing, swimming and volleyball teams.
In a tweet on Friday, the team said it was “in mourning”.
The Ninho de Urubu (“Vulture’s Nest” – so named because the symbol of the club is a vulture) centre underwent a major expansion last year, with the club spending 23m reals (£4.8m, $6.2m), Reuters news agency reports.
The site features accommodation for young players, several pitches, an aquatic park, a gym, a medical centre and a mini stadium.
The club were due to play their rivals Fluminense on Saturday. The game has been postponed, and other clubs have expressed their condolences.
Real Madrid player Vinícius Júnior, who also played for Flamengo, tweeted a crying emoji, writing, “Such sad news. Pray for everyone. Strength strength, strength.”
Just over two years ago, Brazil’s football world was rocked by disaster when a plane carrying top football team Chapecoense crashed in Colombia.
Of the 77 people on board, 71 lost their lives.