Three people were also injured when the fire broke out at Ninho de Urubu, the training ground of Flamengo football club, in Rio de Janeiro.
All ten victims are said by local media to be young athletes. The cause of the fire is not yet known.
Flamengo is one of Brazil's biggest and best-known clubs internationally.
Real Madrid player Vinícius Júnior, who played for Flamengo, tweeted a crying emoji, writing, "Such sad news. Pray for everyone. Strength strength, strength."
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 players aged between 14 and 17 are known to have used the dormitory.
The injured were taken to a nearby hospital, firefighters say.
Who are Flamengo?
Some of its 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.
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.