The injured were taken to hospital with second and third-degree burns, but no life-threatening injuries.
Teck Resources said in a statement the fire happened in the pulverizing room of the mine's dryer complex, where coal is prepared for shipment.
Al Hoffman, chief inspector with the province's Ministry of Energy and Mines, said two inspectors arrived at the mine Sunday and started investigating what caused the fire.
"We may have to send more specialists, depending on what we think the ignition source was."
Hoffman said flash fires like the one in the Greenhills incident were a part of most coal mining operations.
"It's not uncommon to have small operational-type explosions or what they call 'pops' at one of these dryer plants," he said. "They'll want to determine why there was coal dust in the air and what ignited it."
He said it could take several days or weeks to answer that.
"The good thing is, luckily no one was killed," he said. "We're always concerned when workers are injured and we'll be working very hard to determine what the causes of the incident were."
Chris Stannell, a Teck Resources spokesman, described a flash fire as a sudden ignition or burst of flame that was quickly extinguished.
He said mine operations were temporarily suspended, but there was no significant damage and he added the mine would reopen shortly.
No one was in the pulverizing room when the fire broke out, but the three workers hurt in the fire were nearby.
Stannell said the Greenhills Operation, eight kilometres northeast of the Elkford in southeastern British Columbia, is a non-union mine.
He said everybody on site when the fire occurred was accounted for.
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