Eight people inside the home evacuated before crews arrived at the scene.
The fire at the apartment complex off Tazwell Drive caused about $100,000 in damage.
Fire officials were called to the 7200 block of Alameter Court around 2:45 a.m. on reports of a structure fire with a rescue.
According to LMPD spokesman Aaron Ellis, it happened on Taylor Boulevard around 3 p.m.
Officials could not provide any other details, and it is unknown if a car has been located.
The death toll and number of injured is expected to go up, according to Kentucky Gov. Andy Beshear.
The fire broke out in the 4200 block of Monticello Avenue early Tuesday morning.
Firefighters responded to a home in the 3000 block of River Park Drive around 1:30 a.m. on reports of a fire and a possible shooting.
A docking bay fire at a Louisville business caused a large cloud of smoke in the area Tuesday afternoon.
It took 31 firefighters around an hour to control the blaze.