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Harmony said authorities were immediately informed and an investigation was underway.
CEO Peter Steenkamp said executives and management expressed sincerest condolences and said the company was striving to achieve zero harm.
"We believe that our proactive safety culture that has been reinforced through various initiatives is the responsibility of each and every one of our stakeholders at Harmony," he said.
The latest fatalities are the seventh and eighth reported by the gold miner this calendar year.
The first was a fatality at Tshepong in January.
The Association of Mineworkers and Construction Union said it was "dismayed" to learn of the latest fatalities and reiterated fall of ground was the chief cause of fatalities in South Africa's mining industry.
It said the Department of Mineral Resources and Energy's provisional fatality figure was reported at 37 and injuries at 1,053 for the year-to-date at September 28, whereas AMCU's fatality figure stood at 42, including the latest Harmony fatalities.
While the industry's safety performance showed a significant improvement with a 37% reduction in the number of fatalities in 2019, the Minerals Council South Africa and its members could not rest until it achieved its goal of zero harm, CEO Roger Baxter said in a Facts and Figures handbook released last week.
Harmony has strengthened its position as the country's largest gold producer, taking control of AngloGold Ashanti's Mponeng and Mine Waste Solutions this month after completing an acquisition announced earlier this year.
