A news site affiliated with the east Ukrainian separatist said the accident occurred in Donetsk city's vast Zasyadko coal mine.
The region is controlled by separatist fighters and it was impossible to immediately verify the report.
Zasyadko is one of east Ukraine's largest coal mines. It employs 10,000 people when fully operational and has been beset by problems in the past.
A 2007 disaster claimed the lives of more than 100 people and remains post-Soviet Ukraine's worst industrial accident.
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"There are problems with the air ventilation but their lives are not in danger," the agency quoted one Donetsk district official as saying.
"The elevators are not working so they are unable to get out," the regional official said.
It was not immediately clearly how long the power outage might last.
There was no immediate comment from Ukrainian government officials on the rebel report.