Race Across The World is the latest show to be disrupted by the outbreak of the coronavirus.
The regular edition of the programme – which sees teams of competitors trying to travel thousands of miles without hopping on a plane – started at the weekend.
However, filming on the upcoming celebrity special has not yet started, and it has now been postponed as a result of the pandemic.
A BBC spokeswoman said: “Celebrity Race Across The World involves contestants travelling across a number of different countries, and given that official advice in relation to specific countries is continually changing in line with the spread of Covid-19, Studio Lambert has decided to delay production on this series in consultation with and supported by the BBC.”
The spokeswoman said they would “continue to review all productions on a case by case basis following the latest news and advice from the Foreign Office, World Health Organisation and Public Health England”.
The first series of Race Across The World aired in 2019.
It returned to BBC Two on Sunday for a second series, with the contestants tasked with racing from Mexico City to Ushuaia in South America.
The celebrity spin-off promises to see stars – who have yet to be named - “stripped of mod-cons and luxuries”.
They will have to “rely on their skills, cunning, ingenuity and talent rather than the privileges and perks of fame in order to succeed”.
The coronavirus outbreak started late last year and so far there have been more than 118,000 cases globally.
The outbreak was a factor in the new James Bond movie No Time To Die being delayed by several months and many music stars have postponed shows.
Production on TV show Riverdale has been temporarily suspended after a member of the team came into contact with someone with the illness.