Rescue workers are still searching for the other three, it said.
The accident occurred Friday morning at the Kusasalethu mine, about 80 kilometres (50 miles) west of Johannesburg, after an earth tremor about 3,100 metres (10,200 feet) below the earth's surface.
"A second miner trapped at... Kusasalethu mine near Carletonville since Friday morning has been brought to surface. Regrettably, he succumbed to his injuries," the operator, Harmony Gold, said in a statement.
There were 73 deaths in South African mines last year, down slightly from 77 in 2015.
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