The death toll is expected to rise, Beshear wrote in a post on X. Several other people are reported to be injured, some very seriously.
"Please pray for the affected families, Louisville and all of Kentucky. We are devastated now after a heartbreaking day," Beshear wrote.
The plane belongs to the package distribution company UPS and is believed to have crashed shortly after takeoff, according to the US aviation authority FAA, which is investigating the incident together with the aviation safety authority NTSB.
Footage from the scene shortly after the crash shows a fire spreading on the ground as a thick column of smoke rises into the sky. The public is urged to stay indoors.
The crash occurred at 5:15 p.m. local time. The plane was en route to Honolulu, Hawaii.
All flights to and from Louisville Airport, UPS's global hub, have been temporarily suspended.
