Bodies were found at the Enyobeni Tavern early on Sunday, and reports say several people were injured.
"The circumstances surrounding the incident are under investigation as we speak," a police spokesman told the Newzroom Africa television channel.
"We do not want to make any speculations at this stage," Brigadier Tembinkosi Kinana said.
A large number of emergency service personnel are on the scene in the Eastern Cape province.
Relatives of the victims have been unable to see their bodies, reports say, and locals have called for the venue to be closed.
Eastern Cape Police Commissioner Nomthetheleli Lilian Mene told SABC News that "there was an alleged stampede inside the tavern".
South Africa's Minister of Police Bheki Cele was on his way to the Eastern Cape with an additional team of experts to help with investigations, the province's premier Oscar Mabuyane said.
"We can't believe it... Young people who were not sick, young people who should be with their families enjoying their winter holidays - they just have lost their lives like that," he added.