"There are increased costs to pay protection services staff overtime, damage to property, and losses occasioned by the loss of production because non-striking workers are being prevented from going to work," Amplats spokeswoman Mpumi Sithole told Reuters.
"There is evidence of illegal actions of violence and intimidation and breaching of the picketing rules," she said.
AMCU president Joseph Mathunjwa told public broadcaster SAFM that Amplats was "trying to break the strike."
Sithole said the Amplats lawsuit papers had been filed on Friday at a regional high court in Pretoria, but she could not say when the case would start being heard.
AMCU spokesman Jimmy Gama said the union had not received the papers yet and could not respond until it did. The union has always denied allegations that it uses intimidation.
An AMCU shop steward was killed in a clash with police at an Amplats mine on February 7 and the company said at the time that the strike was becoming violent and that several of its vehicles had been damaged.
AMCU has emerged as the dominant union on South Africa's platinum belt over the past two years after poaching tens of thousands of members from the National Union of Mineworkers (NUM), which is allied to the ruling African National Congress.