The attack took place on Wednesday night in the city of Thornton, reports The New York Times.
The police has warned people in the area to stay away from the shopping centre.
Streets leading to the area were blocked by emergency vehicles and police officers armed with guns standing at intersections.
No other details of the gunman were immediately available.
This incident comes after Sayfullo Habibullaevic Saipov on Tuesday drove a pickup truck down a busy bike path in New York’s Lower Manhattan area, killing eight and injuring 13. He was shot by police and then hospitalised.
US federal prosecutors have filed terrorism charges against Saipov.