According to witnesses, police opened fire on strikers armed mostly with clubs and machetes.
The Lonmin-owned platinum mine has been at the centre of a violent pay dispute, exacerbated by tensions between two rival trade unions.
Violence during the strike had already killed 10 people.
Speaking to local radio, police minister Nathi Mthethwa confirmed the death toll, adding: “A lot of people were injured and the number keeps on going up.”
The incident is one of the bloodiest police operations since the end of the apartheid in South Africa.
Police were sent to intervene after several thousand miners gathered at Marikana, which lies about 100 km (62 miles) north-west of Johannesburg, to call for a pay rise of more than $1,000 a month.
The circumstances that led police to open fire remain unclear, but reports from eyewitnesses suggest the shooting took place after a group of demonstrators rushed at a line of police officers.
One witness, Molaole Montsho, of the South African news agency Sapa, said police had first used water cannon, tear gas and stun grenades in an attempt to break up the protest.
“And then in the commotion – we were about 800 m (2,600 ft) from the scene – we heard gunshots that lasted for about two minutes,” he said.
Police ministry spokesman Zweli Mnisi said an investigation into the incident had begun.
Speaking on Thursday, President Jacob Zuma said he was “shocked and dismayed at this senseless violence”.
“We call upon the labor movement and business to work with government to arrest the situation before it deteriorates any further,” he said.
“I have instructed law enforcement agencies to do everything possible to bring the situation under control and to bring the perpetrators of violence to book.”
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