In a message on his Instagram account, 26-year-old Dybala said he and his girlfriend both have the virus but were in good health.
“Both Oriana and I have tested positive,” Dybala said.
“Luckily we are in perfect conditions.”
AC Milan technical director Maldini and his son Daniel both tested positive and a club statement said they “are well”.
The club added that Daniel Maldini, 18, had been training with the AC Milan first team and that he and his father, 51, had spent two weeks in self-isolation at home and would remain in quarantine “until clinically recovered”.
Dybala is the third Juventus player to be confirmed to have the virus, following centre-back Daniele Rugani and France World Cup winner Blaise Matuidi.
Dybala is currently asymptomatic and self-isolating at home.
Italy’s top-flight football league, Serie A has been postponed until April 3 as the global sporting calendar has been jolted by the coronavirus outbreak.