The suspect was no longer believed to be on the scene, the City of New Albany said in an online statement, Reuters reported.
Police locked down the warehouse of personal care brand KDC/One in response to the shooting, the city had earlier said. The suspect's identity was still unknown.
The five victims have been taken to hospital for treatment, New Albany's Chief Communications & Marketing Officer Josh Poland said.
KDC/One provides solutions to many brands in the beauty, personal care, and home care categories.