Responsible Travel, based in Brighton, specialises in wildlife holidays and says keeping animals in zoos is inhumane.
About half a dozen tours that involve zoos are being dropped from the firm's roster of 3,500 possible trips.
The firm's boss, Justin Francis, took the decision after watching a BBC TV programme "Should we close our zoos?"
"Having watched the programme my firm conclusion was that these zoos are no longer relevant," he told the BBC.
"They are relics of the past, and the arguments to justify keeping animals in captivity no longer stand up."
Mr Francis argued that most animals kept in zoos were not endangered and that there had been few examples of endangered species being reintroduced to the wild after being kept or bred in captivity.
Most of the zoos involved in the firm's decision are in southeast Asia and none are in the UK.
The travel company markets about 3,500 tours from 350 operators in the UK and abroad.
It stopped offering tours involving elephant rides about 18 months ago.
It will still sell holidays that include trips to rescue centres, animal rehabilitation centres and breeding centres for endangered species.
Mr Francis explained that it had taken two staff six months to research the zoos and other destinations being offered in his clients' holidays.
Identifying the zoos had taken just a couple of weeks, but scrutinising the other animal facilities on offer to travellers had taken much longer.
The decision to weed out trips to traditional zoos was welcomed by a wildlife charity, the Born Free Foundation.
"[Our] investigations have, over the years, demonstrated that few animal species can adapt to a lifetime in captivity, with many individual animals developing abnormal behaviour, not seen in their wild counterparts, in order to cope with captivity's restrictive and often barren environments," said the president of Born Free, Will Travers.
"A global shift in public consciousness, a movement, may see - if not an end - a massive reduction in the exploitation of wild animals in their millions in thousands of zoos worldwide," he added.
Mr Francis said none of the tour operators whose holidays had been dropped had objected to his decision.
"They told us they hadn't thought things through but now they have been presented with the evidence they agree", he said.
A leading marketer of "responsible tourism" has decided to stop selling tours that include visits to zoos.