The fire broke out at Ninho do Urubu, a state-of-the-art training center that was expanded and opened only two months ago.
It was not known if any players were hurt in the blaze, although the club has accommodation for teenage players at the ground.
“The kids from the Flamengo youth team were sleeping there at the time,” firefighter Douglas Henaut told Globo News.
The fire followed days of heavy rains that hit the city and killed at least six people.
The alma mater of players such as Zico, Junior and Leonardo, Flamengo is one of the best-supported clubs in Brazil and is well-known around the world.