Mine officials said they are believed to be safe.
Marshall Hamilton, a spokesman for Mosaic Company, the US-based firm that operates the mine, said the fire broke out early this morning about 1.6km underground.
The miners reported smoke and then headed for safe refuge rooms where they waited for fire-fighters to quench the blaze and air quality in the mine to improve.
"In those refuge stations, they can seal themselves off and there's oxygen, food and water," Mr Hamilton told CBC Radio.
"And they can stay in there for at least 36 hours," he added.
However, Mr Hamilton said company officials had not been able to establish a radio link with 30 of the miners.
It was not immediately known what caused the fire at the mine.