"Lonmin operations are suspended this morning due to an illegal work stoppage," Lonmin spokeswoman Sue Vey told AFP, adding that work had stopped at all of the firm's 13 shafts in the northwestern Rustenburg mining town.
The workers were singing and dancing on the streets, according to a witness.
The reasons for the strike were still unknown amid growing union rivalry in the region where 34 miners were last year gunned down by police during a wildcat strike at Lonmin's Marikana mines.
Steven was due to testify at a judiciary enquiry into last year's killings by police of striking mineworkers, an incident which shocked the world and brought back memories of apartheid police brutality.
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Rival union the National Union of Mineworkers meanwhile (NUM) alleged the striking workers were intimidating its representatives.
"There is intimidation and violence. They are singing and dancing and have blocked roads. Cars are being turned away. Its really bad," Mxhasi Sithethi, a regional coordinator for the NUM said from Rustenburg.