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Rio will curtail production at Richards Bay Minerals by midnight on Thursday.
The titanium operation was previously suspended for five weeks late last year due to security issues.
Rio will make arrangements for furnaces to be put on care and maintenance in order to avoid damage to their continuous operations, and is yet to resume construction of the Zulti South project.
The company said it was too early to speculate when operations would resume or what the impact on guidance would be.
Rio will also reduce activity at its aluminium operations in Quebec, in line with government orders.
"The health and safety of our people is Rio Tinto's key priority and we are supportive of the action being taken by various governments to address the threat of COVID-19," Rio CEO Jean-Sébastien Jacques said.
"We will continue to work with our employees, customers, communities and suppliers to minimise any impact of action being taken to reduce the spread of COVID-19."
South African manganese producer Jupiter Mines will also suspend the Tshipi Borwa mine, which shipped 3.4 million tonnes in the 12 months to February 29.
The company will assess the impact with its partners.
Developer Orion Minerals has closed its Prieska copper-zinc site and is completing the updated feasibility study remotely.
The company has postponed project financing activities until market conditions stabilise, but is continuing discussions with parties over a potential project-level equity investment.
"While we have made the decision to postpone debt financing activities for Prieska until global market conditions stabilise, we are fortunate that the company will shortly be finalising its active feasibility study work and permitting activities, with a resultant reduction in spending requirements," Orion managing director Errol Smart said.
"We will be able to weather the storm by dramatically reducing spending, while preserving a top-class, build-ready base metal project that can be activated as soon as global manufacturing and metal demand recommences."
Other big miners to be impacted by South Africa's move include Glencore, Anglo American, Gold Fields, Sibanye-Stillwater and Harmony Gold.