The cutbacks represent a huge reduction in Lonmin's workforce, which was 28,000-strong last year, and will add to South Africa's unemployment woes as the country struggles with weak growth.
"The Board is taking firm action to further reduce Lonmin's cost base in the current pricing environment so that it will be able to sustain a viable operation," the company said.
"A total of 6,000 employees including contractors are likely to be affected by (shaft) closures... It is our intention to achieve this outcome in partnership with our employees, unions and other relevant stakeholders."
South Africa produces 70 percent of the world's platinum, and has been badly hit as prices have dropped 14 percent since May, and 45 percent since the start of 2011.
"Our objective is to save the majority of the positions in the company and create a sustainable business by taking urgent action," Lonmin said.
Lesetja Kganyago, governor of the South African Reserve Bank, on Thursday revised growth forecasts down to two percent in 2015 and 2.1 percent in 2016.