The 18-year-old, who joined Dortmund on a two-year loan deal from Real Madrid in August, underwent PCR tests for COVID-19 upon his return from international duty with Brazil Under-23s last week.
Reinier was not part of Dortmund's squad for their Bundesliga win over Hertha Berlin at the weekend and no other BVB players have tested positive.
Borussia Dortmund player, Reinier, has tested positive for COVID-19 and is symptom free.— Borussia Dortmund (@BlackYellow) November 23, 2020
We wish him a healthy and speedy recovery 🙏 pic.twitter.com/xmEG6tzcu7
Dortmund confirmed the news on Tuesday (AEDT), a day before its UEFA Champions League match with Club Brugge, and added that the teenager is asymptomatic and is now self-isolating.
He has been used seven times by Lucien Favre, each of those appearances coming from the bench.
Reinier, who won the Campeonato Brasileiro and Copa Libertadores with Flamengo in 2019, has yet to score, assist or create a chance in his three Bundesliga outings and has managed just one shot.
Wednesday's meeting with Brugge is the first of three home games in a row for Dortmund, with Koln and Lazio to come in the next nine days.