After a review of evidence, including a surveillance video, officers determined there had been an argument in the office of a home health-care business, Capt. Michael Sack told reporters.
The shooting occurred at the Cherokee Place Business Incubator, CNN affiliate KTVI reported.
The victims were two women and two men, described as being in their early 40s to mid-50s, police said. One of the men was the shooter. All of them were believed to be employees.
A semi-automatic handgun was recovered.
Police have not been able to find any witnesses to the shooting, according to Sack.
After receiving a call at about 1:30 p.m., police rushed to the building, which houses several businesses.