"The global situation regarding COVID-19 is fluid and very difficult to predict and it's right we take time to assess the situation and make the right decisions," F1 chief Chase Carey said in a statement.
"We are taking this decision with the FIA and our promoters to ensure the safety of everyone involved in Formula 1 and our fans."
Formula One and the FIA, world motorsport's governing body, said they "expect to begin the Championship in Europe at the end of May but given the sharp increase in COVID-19 cases in Europe in recent days, this will be regularly reviewed."
The Dutch Grand Prix is the next race on calendar, although its scheduled May 3 date will be pushed back. The Spanish Grand Prix in Barcelona was planned for the following week.
The future of the Australian race, the first of the season, was in doubt Thursday when McLaren pulled out after one of its team members tested positive for the virus.
McLaren revealed Friday that 14 other staff were now in a mandatory two-week quarantine after being in close contact with the man.
The McLaren employee was among eight Formula One personnel who went into isolation after showing flu-like symptoms typical of the disease this week.
The other seven - including four from the Haas team - all returned negative results.