Kentucky State Police Capt. Greg Baird said the blaze destroyed three mobile homes owned by the same family one used for living space, the other two for storage. There were 14 people inside the dwelling at the time of the fire, he said.
Seven people were taken to an area hospital in Glasgow with non life-threatening injuries. Two more were flown to University of Louisville Hospital, police said.
"It's like it's not real," said Rhonda Ennis, a relative who said she lives in the nearby town of Edmonton.
The mobile home was in Sulphur Well, a rural community about 100 miles south of Louisville.
The children were ages 1, 2, and 3 and a fourth child was 11 or 12, State Fire Marshal spokeswoman Ricki Gardenhire said.
Baird said the fire was reported around 2:20 a.m. The cause was still being investigated, although he said there were no early indications that it was suspicious. It wasn't immediately clear whether the home had a smoke detector.
The brick foundation of one mobile home were still smoldering hours later. A second, heavily damaged unit was situated adjacent to the first in an "L" shape.
A third home nearby had the least damage but its windows were blown out.
A sign on the side of a barn on the property said, "We do work on small and large motors."
State police had not yet released the names of the victims.