Amplats said three weeks of illegal strikes by 28,000 workers in Rustenburg had cost it 700m rand ($82m; £51m) in revenue.
South African mining has been hit by a wave of wildcat strikes in which miners and officials have been killed.
Thirty-four platinum miners were shot dead by police on 16 August.
A separate strike is continuing at another mining firm, GoldFields, which is the world’s fourth-largest gold miner.
On Tuesday, GoldFields evicted 5,000 striking employees from company dormitories, saying they were intimidating fellow workers.
In all, about 75,000 miners are currently on strike in the gold and platinum sectors, most of them illegally, analysts say.
With unemployment in South Africa already at 25%, the mass dismissal will deal a blow both to the country’s weak economic growth and to President Jacob Zuma’s reputation as leader, says the BBC’s Milton Nkosi in Johannesburg.
The governing ANC party is holding a leadership contest in December, and some members are already calling for Mr Zuma to be replaced by his deputy, Kgalema Motlanthe.
Explaining its decision on Friday, Amplats said the miners had failed to attend disciplinary hearings and had therefore been dismissed.
Attendance levels of less than 20% meant four of the company’s mining operations in Rustenburg could not operate properly.
Employees would learn the outcome of disciplinary hearings later on Friday, and would have three days to appeal over their outcome, said the company.