The government said it would move "very swiftly" against anyone involved in an illegal gathering or carrying weapons, the BBC reported.
Justice Minister Jeff Radebe declined to call the government's planned actions a state of emergency, but the military has been placed on high alert.
A strike last month at the Marikana platinum mine turned violent as police shot and killed 34 miners.
On Friday, hopes for an end to the strike there were unrealized when workers rejected a pay offer from management.
Miners are pushing for monthly pay of $1,513. They currently receive between $484 and $605 monthly. The Lonmin offer would have given the miners an additional $121 a month.
Entrances to the Anglo American Platinum mine were blocked by protesters Wednesday, and on Thursday 5,000 workers at the mine gathered at a soccer stadium near the mine to demand their wages be raised to $1,950 a month, The Wall Street Journal reported.
Anglo Platinum has closed five of its mines. The company said it will discuss miner's demands at a Sept. 25 meeting, and workers say they will be on strike until then.
President Jacob Zuma on Thursday urged mine workers to end their strike, which he said would "make them and the country worse off."
He also urged mine owners to improve living conditions for their workers.
An estimated 54,000 workers have not shown up for their jobs, The Daily Telegraph reported.
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