After a review of evidence, including a surveillance video, officers determined there was an argument in the office of a home health-care business, Capt. Michael Sack told reporters.
The shootings occurred at the Cherokee Place Business Incubator, CNN affiliate KTVI reported.
Two women and two men died, police said. Sack described them as being in their early 40s to mid-50s.
The weapon believed to be used in the shootings was recovered.
Police: Four fatally shot in St. Louis business - CNN.com