One person was in critical condition after the early shooting this morning, said New Orleans police spokesman Frank Robertson. Seven others were hospitalised in stable condition. The remaining victim's condition was not available.
The victims were shot just two blocks from historic Jackson Square and just around the corner from the popular Pat O'Brien's piano bar.
An investigation is ongoing. Robertson said no arrests have been made, and no suspects have been identified. Robertson said other details will be released when they become available.
"Our No. 1 priority is to keep New Orleans safe," Landrieu said in a statement issued through City Hall spokesman Tyler Gamble. "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."
Today morning's incident is the third major shooting on Bourbon Street in the last three years.
Last February 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.
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.