Real Madrid said "it has been decided to close the facilities at our training ground and it is also recommended that all Real Madrid personnel who work there remain in quarantine."
Serie A in Italy, the European country worst hit by the virus, has already suspended its matches until April 3 while France's Ligue 1 will continue its season but without spectators.
Preparations for the Formula One season-opening Melbourne Grand Prix were in chaos after the McLaren team withdrew from Sunday's race when one of its staff tested positive for the virus.
In the United States, the NBA suspended its season after a Utah Jazz player, thought to be Rudy Gobert from France, tested positive for coronavirus.