With details still scarce hours after the shooting, authorities described the injuries as life-threatening, with police on the lookout for a white Ford car, the report said, Reuters reported.
The incident was the third multiple shooting reported within 24 hours in the United States, already on edge over a surge in shootings in recent weeks.
A gunman killed eight workers and himself at an Indianapolis FedEx center on Thursday night, with at least seven deadly mass shootings in the United States over the past month.
In Sunday's Shreveport incident, four people were outside the store, in Hearne Avenue, while one person was inside the store when the shooting happened, according to the KLSA report.
Multiple police units were dispatched to the scene of the incident, which happened around 9 p.m. local time Sunday, the report said.
Reuters was not immediately able to contact local police. The Shreveport mayor's office didn't immediately respond to Reuters' request for comment.
Earlier on Sunday, three people died at an apartment complex in Austin, Texas and authorities were hunting for a former deputy sheriff wanted in connection with the fatal shooting. Separately, three people were killed and two wounded in a shooting at a bar in Kenosha County, Wisconsin, in the early hours of Sunday.
The spate of shootings has increased public pressure to tighten gun regulations. Most Americans support tougher gun laws, according to Reuters/Ipsos polling, but Washington has done little to address the problem in recent years.
RHM/PR