Andy Beshear said the figure could rise to more than 100 in what he called the worst tornadoes in the state’s history.
Dozens are feared dead inside a candle factory in the town of Mayfield.
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.
He also described how two children were reported missing during a tornado but were then found in a bathtub that had been pulled outside by the force of the wind.
“There were two children in the Barnsley area that were missing and they were actually found in a bathtub not where the house was originally standing,” he said.
The Amazon warehouse in Edwardsville in southern Illinois was damaged during a tornado on Friday night, the authorities said.
It is not yet clear how many people were hurt by the roof collapse, but local emergency services have called it a “mass casualty incident” on Facebook.
Illinois police chief Mike Fillback said at least one person had died.
Sarah Bierman said her partner was still missing.
“I talked to him about 8 o’clock tonight, a little before I texted him, and he was returning to the warehouse to drop his van off. And I haven’t heard from him since,” she told the Reuters news agency.
“I decided to come down here to see what was going on. I had no idea the building looked that bad. And I’m just … I’m worried sick. I just want to know if he’s okay,” she added.
“My prayers are with the people of Edwardsville tonight, and I’ve reached out to the mayor to provide any needed state resources,” Illinois Governor JB Pritzker tweeted.
Later reports said 30 people had been rescued and two were airlifted to hospital in St Louis, in neighbouring Missouri. Rescue teams are still sorting through the rubble.
Tennessee state Emergency Management Agency spokesman Dean Flener said three people had been killed in the northwest of the state. No further details were given.
In north-eastern Arkansas, one person died, five were seriously injured and 20 people were trapped inside in a nursing home after it partly collapsed, local official Marvin Day said.
The trapped people were rescued but the building was “pretty much destroyed”, he added.