McLaren withdrew from the season-opening Australian Formula One Grand Prix in Melbourne on Thursday after a team member tested positive for coronavirus, fuelling concerns about the race going ahead.
The British-based team, whose drivers are Spaniard Carlos Sainz and Briton Lando Norris, did not reveal details about the employee.
"The team member was tested and self-isolated as soon as they started to show symptoms and will now be treated by local healthcare authorities," the former champions said in a statement.
"The team has prepared for this eventuality and has ongoing support in place for its employee who will now enter a period of quarantine. The team is cooperating with the relevant local authorities to assist their investigations and analysis."
McLaren said they had made the decision "based on a duty of care not only to McLaren F1 employees and partners, but also to the team's competitors, Formula One fans and wider F1 stakeholders."
There was no immediate comment on McLaren's participation in the March 22 Bahrain Grand Prix, something of a home race for a team majority-owned by that country's Mumtalakat sovereign wealth fund.
Tests on four Haas team members who had been quarantined due to the outbreak came back negative, a spokesman said.
US-owned Haas are also British-based but have close ties to Ferrari, the Italian team whose engines they use.
Victoria state's top health official had warned earlier that positive tests in the paddock could lead to the race being scrapped.
"If (the tests) turn up positive, we need to consider what it means for their close contacts and if they have a number of close contacts across a number of crews, then those individuals need to be quarantined," Brett Sutton told Melbourne radio station 3AW.
"If that effectively shuts down the race, then so be it, we'll make that call."
Mercedes' six times world champion Lewis Hamilton told reporters earlier that it is "shocking" the race could go ahead and suggested organisers had put financial concerns ahead of people's health.
Italy, Europe's worst affected country, is in lockdown to fight the coronavirus, and the run-up to the race weekend had been dominated by uncertainty over the Italian teams' ability to attend.
Thousands of fans poured into Albert Park on Thursday as race-week kicked off with practice and qualifying for lower-profile motor sport circuits.
The Chinese Grand Prix, which was scheduled for April, has been postponed while Bahrain is scheduled to take place without spectators.
The Vietnamese Grand Prix, third race on the calendar, is also looking uncertain.