Writing in The Daily Telegraph, Vaughan said the prospect of Australia facing an understrength England team "would be farcical", with senior players considering not travelling unless their families can visit over the Christmas period.
"If this situation is not sorted out quickly and the England players allowed to be joined in Australia by their families then the Ashes have to be delayed by a year," Vaughan wrote.
"If not, it would be a farcical series against an understrength England team.
"The Ashes must be the best against the best."
Australia has put in place some of the world's most stringent travel restrictions in an attempt to keep the virus at bay, with tight limits on the numbers permitted to enter the country.
England are due to start the first match of the five-Test series against Australia on Dec 8, with the final meeting to be played from Jan 14 to 18.
On previous Ashes tours, players' families have joined them over the Christmas period, but similar arrangements would be complicated by Australia's quarantine regulations.
The difficulties are amplified by key players such as Ben Stokes and Jos Buttler facing the prospect of being away from home for four months due to their involvement in October's Twenty20 World Cup.
Australia recently withdrew from the Rugby League World Cup in England in October due to COVID-19 concerns, while seven of the country's cricketers refused to take part in a just-completed West Indies tour.
"I have absolute sympathy with any player thinking of not going and I would back them all the way if they pulled out because they cannot be with their families at Christmas and New Year," wrote Vaughan.
"We need the Ashes. But we need the series to be fair and competitive."