Ministers from WTO members were due to have gathered next week for a meeting widely seen as a test of the WTO's relevance.
The WTO said that its members had agreed late on Friday to postpone the ministerial conference after the new variant outbreak led to travel restrictions that would have prevented many ministers from reaching Geneva.
No new date has been set for a rescheduled meeting.
The World Health Organisation has classified the B.1.1.529 variant detected in South Africa as a "variant of concern", saying it may spread more quickly than other forms of the virus. Scientists are also seeking to find out if it is vaccine-resistant.
Switzerland, home to the WTO, on Friday banned direct flights from South Africa and the surrounding region, and imposed test and quarantine requirements on travel from other countries, including Belgium, Hong Kong and Israel.
The Geneva-based trade body had planned a meeting in person, but the new restrictions meant delegations of large players such as South Africa and the Brussels-based European Commission would have been limited to a largely virtual presence.
Even before the postponement the prospects were not bright.
The WTO has only managed one update of its global rules in its near 27-year history, the red tape-cutting Trade Facilitation Agreement, and its 164 members looked far from agreement in its most active talks - on curbing fishing subsidies and spreading COVID-19 vaccines more widely.
India, South Africa and other developing countries are calling for a waiver of intellectual property (IP) rights for vaccines and other COVID-19 treatments. U.S. President Joe Biden said on Friday he supported a waiver for vaccines.
WTO Director-General Ngozi Okonjo-Iweala said the postponement did not mean negotiations should stop.
"On the contrary, delegations in Geneva should be fully empowered to close as many gaps as possible. This new variant reminds us once again of the urgency of the work we are charged with," she said in a statement.
Santiago Wills, the Colombian WTO ambassador who chairs the fishing subsidy talks, said the news was "deflating, to say the least", but pledged to keep working towards an agreement to save global fish stocks.
(Reporting by Emma Farge and Stephanie Ulmer-Nebahay in Geneva; Writing by Philip Blenkinsop; Editing by Mark Porter and Sandra Maler)