Ferrari said the decision has been made for their “employees' wellbeing".
Chief executive officer Louis Camilleri said: "It is out of our respect for them, their peace of mind and of their families that we have decided on this course of action.”
Other F1 teams are carrying on working for now, while Mercedes team members in Melbourne are in the process of self-isolating for 14 days.
Meanwhile, the Dutch Grand Prix set to be the next race pulled from Formula One's schedule.
There were conflicting messages as to when the new F1 season might start after this weekend's curtain-raiser in Australia was cancelled, with subsequent races in Bahrain, Vietnam and China postponed.
F1's governing body, the FIA, issued a statement to indicate the campaign could get under way at the beginning of May - in time for the race in Holland.
F1, however, said the end of May is now the target. And it is understood that the Dutch round - scheduled for May 3 - would be postponed. Official confirmation is expected at the start of next week.
It is hoped that the Zandvoort race, which returns to the calendar after an absence of 35 years, could be moved to August. The Spanish Grand Prix, due to take place on May 10, is also set to be called off. It is unclear whether it will be rescheduled.
The majority view of the sport's travelling circus is to delay the campaign until the Azerbaijan Grand Prix, pencilled in for June 7, at the earliest, with the possibility of as many as 18 races crammed into six months.