With ongoing uncertainty around the fate of F1's first three races, despite the events in Australia, Bahrain and Vietnam all on for now, Williams says that careful thought needs to be given about personnel and fan movement.
Speaking at an event in London with her team's title sponsor ROKiT, Williams said that the situation was a difficult one for everyone involved.
"It's an incredibly serious situation," said Williams. "Being a global sport travelling around the world with thousands and thousands of people, and that doesn't take into account the number of fans travelling as well, there's so much movement that we've got to be incredibly responsible and enormously responsive as well.
"But at the moment it is a moving target. We're clearly keeping in touch with the relevant authorities, with F1 as well, and taking the guidance as it's coming. But it is changing literally by the hour at the moment.
"It's quite a difficult management piece, when you're thinking about F1 and the number of personnel that you're taking to a race. Plus the amount of kit that you're putting on air freight and sea freight, and the cost involved in all of that.
"We want to go racing at the end of the day, but we've got to make sure that we keep our people safe in doing that. We will just continue to take the guidance as and when it comes through."
Former grand prix driver Felipe Massa says the coronavirus outbreak is a worry for everybody because there is so much uncertainty about how the situation will develop.
"I think it's a little scary moment for everybody," said Massa, who currently races in Formula E.
"We need a little bit more information. The virus is growing, but how serious it is - the right information is something that we are still missing.
"We see that many events have been cancelled, and maybe we will cancel many others if it keeps growing like that, so we just need to take care."
While there has been no change in status for F1's first three races, fresh doubts have emerged about the Vietnam race with the country imposing restrictions on people arriving there from Italy.
The government has advised that arrivals from Italy will be put in quarantine for 14 days – something which could prove troublesome for staff from Ferrari, AlphaTauri and Pirelli if they have returned to base after the Bahrain GP.
It was a similar restriction in Qatar which prompted MotoGP to cancel the season opener there.