Brazil's Ministry of Health said on Monday that 31 players and Copa America delegation members had tested positive for COVID-19 by Sunday, the first day of the South American tournament.
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Another 10 cases were confirmed among employees working at hotels where the players and their delegations are staying in Brasilia, Health Minister Marcelo Queiroga told reporters.
Among the previously known cases were two members of the Colombia delegation, as well as eight from Venezuela and three from Bolivia.
Confirmation of more cases of infection came as the South American Football Confederation (CONMEBOL) defended itself against accusations that the tournament, which was awarded to Brazil with less than two weeks notice, was cobbled together at the last minute.
Speaking before their match against Chile, Argentina star Lionel Messi said the fear of contracting the virus was widespread in the squad.
"It worries us because it is a risk for everyone catching COVID-19," he told reporters on Monday. "We try to be careful but it's not easy. These things happen."
"We'll try to do all we can so no one gets it but sometimes it doesn't depend solely on ourselves."
Brazil was picked after Colombia was withdrawn due to a wave of civil unrest and co-hosts Argentina pulled out because of a surge in COVID-19 cases. The oldest international tournament in the world, the Copa America final is at the Maracana stadium in Rio de Janeiro on July 10.
Information from Reuters was used in this report.