The Airline Highway has been shut down and a police spokesman said the area has been contained, however warned residents to stay away from the area.
A bomb disposal robot is on the scene, checking for explosives.
Louisiana Governor John Bel Edwards said: “This is an unspeakable and unjustified attack on all of us at a time when we need unity and healing.”
Hammond Aire Plaza is around five miles away from the Triple S Food Mart, where street seller, Alton Sterling was shot dead at the hands of police officers earlier this month.
Mr Sterling, 37, was pinned to the ground and shot in the chest outside a convenience store in Baton Rouge, Louisiana, on July 5.