The Serie A side said they are “activating all the isolation procedures required by law”, including for those who have come into contact with Rugani.
The club added that Rugani, 25, is “currently asymptomatic”.
Rugani has made only seven appearances for Juventus this season and was an unused substitute in his side’s last match – a 2-0 win over Inter Milan held behind closed doors on Sunday.
Inter, whose Europa League game against Getafe that was set for Thursday has been postponed, said that “all competitive activities are suspended until further notice” following Rugani’s positive test.
They added: “The club is taking steps to prepare all necessary procedures.”
Rugani has won four Serie A titles with Juve and played for Italy seven times, last featuring for the national team in 2018.
On Sunday he posted a photograph from the dressing room as he celebrated Juve’s win over Inter with his team-mates