National Mine Workers Union head Shadreck Pelewelo said that 20 miners were rescued after the incident which caused a fire at the Mimosa platinum mine.
Mining company Implats said in a statement that the fire has been contained.
Pelewelo told The Associated Press that rescue efforts were "going on well so far" and there were no fatalities.
Executives of the Mimosa Mining Company in Harare were in an emergency meeting and were not taking calls, staff at the company's offices said.
Pelewelo said the breakdown happened around dusk on Monday. He said the trapped men have received food and water.
He said 85 miners were underground at the time and 20 were brought out safely without injury. Pelewelo said he was headed to the mine with other union leaders to assist in support and assessment tasks.
Zimbabwe is the second largest producer of platinum after South Africa. Mimosa Mine is jointly owned by the Mauritius-registered Aquarius organization and South Africa's Impala Platinum known as Implats.
Implats said all employees at the mine were accounted for and none suffered injuries. Those remaining in underground refuge bays are expected to be moved to the surface later todayPost published in: Mining