Many dogs suffer so severely they have trouble exercising for longer than three minutes.
Some dogs find it difficult to moderate their body temperatures through panting and can die from overheating.
The extent and severity of Boas symptoms caused Trade Me to act.
"Research we've seen shows that 90-95 per cent of these dogs have Boas to varying degrees.
"We didn't take this decision lightly," Ryan said, adding that they sought help from the SPCA and the New Zealand Veterinary Association (NZVA).
SPCA chief executive Andrea Midgen says that the dogs deserve better.
"Pugs, British bulldogs and French bulldogs are lovely little dogs, but their exaggerated physical features cause them considerable welfare issues."
NZVA chief executive Mark Ward said they had long held concerns for many breeds of cats and dogs whose welfare is compromised from being bred in a certain way.
The rise in popularity of these dogs has caused those with exaggerated features serious health issues.
"Without correctional surgery, large numbers of these dogs live with chronic pain and distress, with many owners and breeders unaware that their dog is suffering," Ward said.
The dogs have increased in popularity over the years, which has seen an increase in dogs taken to the vet with numerous serious health issues.
Ward said some are unable to reproduce naturally.
""In addition, almost all of these dogs are no longer capable of mating or giving birth naturally.
"This means each litter requires the mother undertake a risky Caesarean section to produce puppies for sale," Ward said.
NZVA hopes that by Trade Me making this stand that potential puppy buyers will take make an informed choice before choosing a pet.
The SPCA asks that Kiwis that are looking to add to their family by getting a pet to consider adopting one of the thousands of rescue dogs they have.
Ryan said Trade Me was not making judgments on current owners of the breeds but sees the ban as an opportunity to educate potential owners.