“Kentucky, we have some tough news out of Martin County to share,” he wrote on X/Twitter. “At least one of the workers trapped inside the collapsed coal preparation plant has died. Please pray for the family and loved ones of this individual.”
The worker who died has not yet been identified.
Rescuers have made contact with the trapped worker, but are still working to retrieve him.
Mr Beshear declared a state of emergency in Kentucky on Wednesday morning, which allowed him to activate more resources to assist in the rescue effort.
He asked for prayers for the affected workers.
“Kentucky, keep praying — but the scene is bad and we should be prepared for tough news out of Martin County," he wrote.
Multiple floors of concrete and steel collapsed while crews were at the Martin Mine Prep Plant demolishing an abandoned mine site near Wolf Creek in Martin County, according to Judge Executive Lon E Lafferty.
The facility had reportedly been out of use for a number of years prior to the accident. The workers were on the building's bottom floor when the structure buckled and the ceiling dropped around 6:30pm.
Martin County Sheriff John Kirk told WRAL that the sheer volume of steel and concrete dropped on the workers will ensure the rescue operation takes days.
“This is a lot of weight. A lot of large metal structures, a lot of concrete, and very confined space last. Very tight spaces,” he said, noting that his office wasn't "really equipped for this type of disaster."
Mr Kirk said workers had spent the past eight months tearing down the facility section by section.
"They typically take these down in sections. They fall them, you know, cut torch and fall them in section," the sheriff told Fox News. "We believe that’s what happened. That it just didn’t fall the way they had projected it to fall and it actually closed around them."
Mr Kirk said he felt a bit "helpless" because there was only so much he could do for the trapped worker.
"You kind of feel helpless that you can’t do more, that you can’t for it faster, but this is not a fast process. It’s a very slow process in order to try to keep everybody safe. This is a rescue mission," he said. "If you pray, pray for these people. Pray for the victims, the families. Pray for the first responders."