Coronavirus testing carried out by Flamengo returned 38 positives, the club has announced.
A total of 293 people associated with the 2019 Copa Libertadores winners were tested for Covid-19 and three first-team players were among those found to have the virus.
The South American and Brazilian champions said all 38 individuals were asymptomatic, while results showed a further 11, two of which were players, had come into contact with the virus previously.
A statement issued by Flamengo said: "Players who have had family members, or employees, with positive tests will enter quarantine, with daily monitoring and questionnaires about signs of the virus and new tests.
"In case of new negative tests, they will be integrated into work in a safe period or, in case of a positive test they will follow, from then on, the standard of conduct of those who have already tested positive.
"Finally, Flamengo reaffirms that it is working in full harmony with government authorities to, with all responsibility and security, work towards the important return to football activities in the shortest possible time."
Flamengo manager Jorge Jesus contracted coronavirus back in March, however his symptoms were week and the Portuguese coach was given the all clear a week later.
Jesus has been linked with a return to European football, with Premier League side Newcastle United said be considering an approach once their long-awaited takeover is complete, however the 65-year-old reaffirmed his commitment to the South American champions last week.
He said: "Right now, I have nothing on my mind. I have to live day by day, know that what happens is because of this epidemic and make decisions.
"We feel like we've created a great team. That's one of the factors that motivates me a lot more to continue, and the way I've been treated too. I have two months to decide my future.
"I feel that Flamengo want me a lot and that is decisive for me, to have a club that wants me a lot."
Flamengo announced on Monday that masseur Jorginho, who had worked at the club for 40 years, died aged 68 due to a cardiac arrest after complications from Covid-19.
Players at the club agreed a 25 per cent pay cut for May and June and could be back in training next week.