Lenny Gilliam, 56, died on Tuesday afternoon at the Huff Creek mine no 1 in Harlan County.
The mine is operated by Lone Mountain Processing, a subsidiary of Arch Coal.
The Kentucky Office of Mine Safety and Licensing said preliminary reports indicated the side of a coal pillar burst as a continuous miner machine was operating, causing the men to be trapped under a collapsed mine wall.
The agency said the incident was reported around noon on Tuesday and the two injured miners were taken to a hospital with non-life threatening injuries.
Mine Safety and Health Administration data showed the mine had been cited three times in July and once in May for roof control plan violations.
The mine was last inspected on July 25, 2013.
The death comes only a day after MSHA cited a reduction in the number of underground mining fatalities from roof and wall collapses.
From 2003 to 2007, 28 miners died in underground roof or wall collapses, compared with 19 between 2008 and 2012, according to a Monday statement from the agency.