Officers were interviewing several witnesses to the incident.
Invercargill resident Caitlin Barton said yesterday she saw a man lying on the footpath as she drove to work.
"He was lying flat as if he had slipped on ice and had a back injury. Lots of people were crowding around him and an ambulance came flying past me ... I didn't think it was a shooting until I saw it on Facebook."
Police asked anyone with information on what happened in the Kelvin St area yesterday morning to get in touch.
They would particularly like to hear from anyone driving on Kelvin St, near the intersection with Earnslaw St, about 9am Saturday.
Phone police on (03) 211 0400, or call Crimestoppers anonymously on 0800 555 111.