In a statement on Twitter, the 23-year-old from Monaco said: "I am feeling OK and have mild symptoms.
"I will remain in isolation in my home in Monaco in compliance with the regulations set by the local health authorities."
Earlier this month, McLaren driver Lando Norris, 21, tested positive for Covid-19 while on holiday in Dubai.
Testing for the 2021 season is scheduled for March, although the date of what should have been the first race has already been pushed back as the Australian Grand Prix has been moved from 19-21 March to 19-21 November because of Covid-19 restrictions.
The first of 23 scheduled races is now the Bahrain Grand Prix from 26-28 March.
Last season, Racing Point drivers Sergio Perez and Lance Stroll and Mercedes' world champion Lewis Hamilton all tested positive for Covid-19.