Booking.com's chief executive Glenn Fogel told the BBC that holiday "prices are already going up".
Many airlines have significantly reduced the number of flights they operate due to travel restrictions.
Despite huge demand, uncertainty makes it hard for airlines to plan bringing more planes back into service, he said.
"There's so much pent-up demand," said Mr Fogel. "Everybody wants to go travelling, but we all want to do it safely."
