The victims were shot two blocks from historic Jackson Square and just around the corner from the popular Pat O'Brien's piano bar. Preservation Hall, a music venue dedicated to preserving New Orleans jazz, is also nearby.
Serpas said at a news conference in the French Quarter that the victims were shot "by two cowardly young men trying to hurt each other."
"What happened was two young men got angry at each other and shot at each other," he said.
Bourbon Street is a nightly swirl of bright neon and tourists, usually with beverages in hand. A blend of jazz joints, strip clubs, bars and restaurants, Bourbon Street has everything from four-star dining to sex shows.
New Orleans Mayor Mitch Landrieu pledged a swift response from law enforcement.
"Our No. 1 priority is to keep New Orleans safe," Landrieu said in a statement. "These kinds of incidents will not go unanswered ... I am confident that between video evidence and eyewitness accounts, we will bring the perpetrators to justice."
Police have not determined whether the shootings might be gang-related, Serpas said. He called on residents, businesses and witnesses who may have video footage, including any from surveillance cameras, to contact police.
It was the third major shooting on Bourbon Street in the last three years.
On the Saturday before Mardi Gras, four people were treated at a hospital after a shooting. During Halloween in 2011, one person was killed and seven others were injured after gunmen opened fire on each other.
Justin Sigalos, of Chicago, was visiting New Orleans with friends this weekend. Standing near the site of the shootings, where blood was still visible on the sidewalk, he said the number of people struck by bullets was surprising.
"That's a lot of people," he said. "Maybe one person getting shot, I could understand. But nine?"
Andrew and Timothy Wiese, brothers from Daphne, Alabama, near Mobile, were walking down Bourbon Street on Sunday with cocktails in their hands. They said they had been on Bourbon Street until a little after midnight.
"We might be cutting tonight a little shorter," Timothy Wiese said. "Late like that, typically bad things happen," his brother added.
Built on higher ground than most of the city, the French Quarter was spared the worst of Hurricane Katrina in 2005, mostly suffering scattered wind and water damage.