The National Union of Mineworkers (NUM) and Association of Mineworkers and Construction Union (AMCU) voted for a strike last week. A smaller union UASA had also voted in favour of a strike.
Another major union of workers, Solidarity split from the coalition last week after accepting Sibanye's final wage offer of a 5% annual pay increase.
NUM and AMCU, the two biggest mine unions in South Africa, have demanded an increase of R1,000 per month over the next three years, similar to the amount Sibanye's rival Harmony Gold agreed to pay last year.
Sibanye's chief executive Neal Froneman said the company would not be revising its final offer, as it could not sustain higher wage increases.
"There are no winners in a strike," Froneman said in a statement on Tuesday.
"We urge employees to carefully consider the consequences of strike action on them personally and collectively. Strike action will only serve to jeopardise the sustainability of our gold operations and, ultimately, their futures."
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