The two men may have been shooting at each other, Thibodaux Police Department Public Information Officer David Melancon told WWL.
The shots were fired at the intersection of Canal Boulevard and Jackson Street around 2:30 p.m.
Both victims were rushed to the hospital but their conditions are unknown.
Officers recovered multiple guns at the scene, reported WDSU.
The Thibodaux Police Department is being assisted by multiple other agencies, including the Louisiana State Police.