Production has been paused.
Vale said the miners were unable to return to surface after a scoop bucket being transported underground on Sunday detached and became hung up in the shaft.
It rendered the usual cage transport system unavailable.
No one was injured and the employees immediately went to refuge chambers, where they were in frequent communication about extraction plans, Vale said.
"The employees are being extracted via a secondary egress ladder system with support of Vale's mine rescue team," the company said.
It expected all 39 to return to surface "in the coming hours".
"We are relieved and delighted to see these individuals returning to surface safe and sound," Vale's head of mining operations for Ontario Gord Gilpin said.
United Steelworkers Union Local 6500, which represents 30 of the 39 trapped workers, was "cautiously optimistic" all would be safely evacuated soon.
President Nick Larochelle said rescue teams had been able to deliver food and medication for certain workers.
"Every effort is being made to ensure everyone is brought back to surface safely and as quickly as possible," Larochelle said.
Ontario premier Doug Ford said their thoughts were with the trapped miners.
"We understand this rescue will take some time and are very relieved to hear the miners are currently uninjured," he said.
Vale said it was assessing the necessary measures to resume production at the site.
Totten produced 3,600 tonnes of finished nickel in the first six months of 2021, representing about 4% of the company's output.
