Seventy-five people, who had been buried in collapsed office buildings and underground, were rescued, Manzini Zungu said.
But three people were still trapped at a depth of 160m in a room where lamps used by miners are handled, with no ventilation and rocks rolling down there, he said.
“The main offices at Makonjwaan Gold Mine in Barberton ... caved in at 8.40am [0640 GMT] this morning”, 350km east of Johannesburg, the union said in a statement.
“It is reported that at the start of the morning shift, the main crown pillar collapsed into the underground open stopes, trapping miners at the mine owned by Vantage Goldfields Limited,” the Department of Mineral Resources said.
Some of those rescued were taken to hospital with injuries, according to Zungu.
Vantage Goldfields said it would issue a statement later.
“We cannot make a pronouncement until our team has done its work. There is a fluid situation on the ground,” said Martin Madlala, a spokesman for the Department of Mineral Resources.
The collapse is the second mining accident within two weeks, following the deaths of four miners in a fire at a platinum mine in Rustenburg, northwest of Johannesburg.
Mining accidents claimed 77 lives in South Africa in 2015, down from 84 the previous year, according to government figures.
AMCU chief Joseph Matunjwa told DPA that current legislation did not provide adequate disciplinary measures for mining companies failing to ensure the safety of their workers.
Victims of accidents often do not get adequate compensation, he said.
Charmaine Russell from the South African Chamber of Mines said that accidents were investigated by government, company and union representatives, and that legislation guaranteed dead victims’ families access to their retirement funds.
An AMCU statement accused the Makonjwaan mine, the mining industry and the government of “absolute criminal neglect towards mine workers” and suggested that cost cutting might have caused the collapse.
The National Union of Mineworkers called on companies “to invest more money in protecting the lives of workers than focusing more on profits”.
“It is worrying that we are seeing such serious accidents so early in the year. We urge all parties to continue prioritising safety,” Mineral Resources Minister Mosebenzi Zwane said.
The mining of gold, diamonds, platinum and other minerals is one of the key sectors in the South African economy, the most industrialised on the continent.
South Africa, one of the world’s largest gold exporters, also has some of the world’s deepest gold mines, which increases the risks for miners.