Varane will also miss this weekend’s key La Liga clash against Barcelona because of his positive test.
The 27-year-old will be a huge doubt as well when the second leg against Liverpool comes around at Anfield next week.
Varane joins Sergio Ramos on the sidelines after the Real Madrid captain returned from international duty with Spain with a calf injury.
'Real Madrid CF informs that our player Raphael Varane tested positive in the Covid-19 test he underwent this morning,' a statement on their official website read on Tuesday.
Varane was expected to play a key role in organising the Los Blancos backline in the absence of Ramos and was rested for last weekend’s La Liga victory over Eibar.
Manager Zinedine Zidane will be left with Nacho Fernandes and Eder Militao as his remaining options for the centre back slots.
Varane has made 36 appearances in all competitions for Real Madrid this season.
He joined the 13-time European champions from French side Lens in the summer of 2011, and has won four UEFA Champions League trophies and three La Liga titles among numerous other honours.