The firm said it had made contact with three of the workers trapped in the Masakhane mine west of Johannesburg and had mobilised rescue teams.
Sibanye-Stillwater produces more gold in South Africa than any other company.
The National Union of Mineworkers (NUM) said it was "angry and concerned at the rate at which mining incidents are happening at Sibanye-Stillwater".
"This suggests that greater attention be paid to issues of safety, particularly the protection of the lives of workers, as opposed to the insistence of chasing production", it said. Driefontein produced 482,000 ounces of gold in 2017, accounting for about a third of Sibanye's output of the metal.
It called for "more serious intervention" to take place at Sibanye Stillwater operations in South Africa. While safety has improved since the end of whites-only rule in 1994, fatalities in the sector increased a year ago for the first time in a decade.
Briton Mike Hodge is dragged away by a lion
Whatever be the noble thought of the man, he found himself under attack from the predator who had nearly gone for the kill. The lion drags a limp Hodge towards some bushes as other park visitors scream for help.
"The Department of Mineral Resources and all the unions have been informed and representatives are on site assisting with the rescue efforts", it noted.
Six of the rescued workers have been hospitalised.
One employee was fatally injured at the Driefontein operations on February 12 and two employees fatally injured at the Kloof operations on February 7.
In February, almost 1 000 miners were trapped underground for 30 hours following a power cut caused by a storm in another mine owned by Sibanye-Stillwater.
Eight miners remain underground, the company said.