The shooting was reported just after 3 p.m. at the Kroger store in Jeffersontown, located on the eastern outskirts of Louisville.
Police Chief Sam Rogers told reporters a suspect entered the store, encountered a man, fired multiple shots at him and left. The suspect then encountered a woman in the parking lot and shot her as well. Both victims were pronounced dead at the scene, Rogers said.
Rogers couldn't speak to a motive and said the shootings were apparently random.
Multiple Kroger employees and employee family members told CBS affiliate WKLY a person came into the store shooting, the station's Lauren Adams reports via Twitter. Witnesses inside the store told Adams they took cover, fearing for their lives.
In a statement released to CBS News, a Kroger spokeswoman said the company is "shocked and saddened" by the shooting.
"Thanks to the quick response of the local police department, the suspect was apprehended and our store is secure," the statement said.
The statement said the store is closed and Kroger is cooperating with law enforcement.
This is a developing story and will be updated.