The entrepreneur said that Virgin Holidays would stop selling and promoting attractions involving “captive cetaceans, such as whales and dolphins”, with SeaWorld parks in San Diego and Florida among those affected.
In a blog post on the Virgin website, Sir Richard said the move was a “significant milestone” in his bid to “drive positive change in the tourism industry”.
SeaWorld has struggled to combat public perception of its parks since the 2013 documentary Blackfish shined a light on the lives of killer whales in captivity.
In a statement, a SeaWorld spokesman said Virgin Holidays had given in to “animal activists who mislead and manipulate marine mammal science to advance their agendas”.
They told Sky News: “Virgin’s own corporate mission is having a measurable purpose that positively impacts communities and the environment. SeaWorld is the epitome of that mission.
“With more than 35,000 animal rescues and decades of meaningful scientific contributions, we are proud to be a recognised global leader in marine mammal science, education and, in particular, providing preeminent care to all of our marine mammals.
“With rising threats to our oceans and their inhabitants, supporting independently accredited zoological facilities is more important than ever. No company does more to protect marine mammals and advance cetacean research, rescue and conservation than SeaWorld.”
SeaWorld parks suffered a decline in attendance following the release of Blackfish, which focused on a captive orca named Tilikum who was involved in the deaths of three people, including a SeaWorld Orlando trainer.
He was captured in Iceland in 1983 and was eventually transferred to the Florida park in 1992, where he stayed until he died at the age of 35 in 2017.
According to animal rights group PETA, Tilikum is one of at least 40 orcas to have died at SeaWorld parks from causes including severe trauma, intestinal gangrene and chronic cardiovascular failure.
Dozens of dolphins have also died at the parks, PETA says.
SeaWorld described Blackfish as “inaccurate and misleading” at the time of its release, and the parks have since recovered in attendance figures thanks to new rides and animal exhibits.
In 2016, SeaWorld also announced it would end its in-park orca breeding programme and eventually phase out theatrical whale shows that have been a staple of its parks for years.
It has also been backed by the Association of Zoos and Aquariums and animal welfare organisation American Humane over the Virgin announcement, which comes a year after Thomas Cook said it would stop selling trips to animal parks where killer whales are kept captive.
The travel agent said the decision was prompted by customer feedback, with more than 90% saying it was “important” that their holiday company took animal welfare seriously.