Two victims were in critical condition and six others were stable, police said. The condition of the ninth victim was unknown.
The shooting happened around 2:45 a.m. local time after the men engaged in a verbal dispute that escalated into gunfire, the department's superintendent, Ronal Serpas, told reporters.
"Nine people were shot as a result of two cowardly young men trying to hurt each other," he said, adding that the pair "chose to settle their dispute with no regard to others."
Bullets ricocheted on the street in front of two well-known New Orleans haunts - Pat O'Brien's bar and jazz venue Preservation Hall, according to the Times-Picayune newspaper.
Police in the area responded "within seconds," Serpas said, and were reviewing numerous surveillance and cell phone video clips of the incident.
One witness told broadcaster WWLTV he heard an argument between the two men before the shots were fired.
The shooter "pulled the gun out and started shooting at the guy, then turned around on the crowd and started shooting at us," the man told WWLTV.
Bourbon Street runs through the heart of New Orleans' oldest neighborhood, the French Quarter, a prime tourist destination packed with bars, restaurants, clubs and souvenir shops.
(Reporting by Victoria Cavaliere in New York; editing by Colleen Jenkins, John Stonestreet and Matthew Lewis) - See more at: http://syndicate.tila.trb/news/nationworld/sns-rt-us-usa-neworleans-shooting-20140629,0,1341814.story#sthash.iY8dyXGH.dpuf