At least five people died as tornadoes wreaked havoc in other states, including one in an Amazon warehouse in Illinois.
Mr Beshear has declared a state of emergency in Kentucky. He said the tornado system was the deadliest to ever run through the state.
Mayfield and everywhere along the 227-mile (365-km) path of the tornado – almost all in Kentucky – was devastated, he said.
“It’s indescribable, unlike anything I’ve ever seen,” he said.
“You see parts of industrial buildings, roofs, or sightings in trees, if trees are lucky enough to stand.
” Huge metal poles bent in half if not broken, buildings that are no longer there, huge trucks that have been picked up and thrown. And sadly far too many homes that people were likely in, entirely devastated.”
” There are a lot of families that need your prayers,” he added.
Deaths had been reported in several counties, but the loss of life in the Mayfield factory could exceed that of any tornado event in a single location in state history, the governor added. More than 100 people were inside when it hit.
Mr Beshear said 40 people had been rescued at the factory and he was praying for more survivors, but it was a “very dire situation”.
Local officials who visited the scene spoke of heavy machinery displaced by the storm, as well as drums leaking corrosive liquid .
US President Joe Biden tweeted that he had been briefed about the tornadoes on Saturday morning.
“To lose a loved one in a storm like this is an unimaginable tragedy,” he said. “We’re working with governors to ensure they have what they need as the search for survivors and damage assessments continue.”
Police said the tornado caused “significant damage” across the western parts of the state. A train was derailed during extreme winds in Hopkins County, Sheriff Matt Sanderson told WKYT-TV.