Police Chief Michael Harrison said the driver, who is suspected of being “highly intoxicated”, was arrested, the Times-Picayune newspaper reported.
New Orleans Mayor Mitch Landrieu said there was no evidence to suspect terrorism, the newspaper added.
“Our thoughts and prayers are with the victims injured by a drunk driver on the parade route today,” Landrieu wrote on Twitter.
The pick-up truck hit three vehicles and a dump truck before it plowed into the pedestrians, New Orleans police said.
“Initial reports show so far about a dozen people are in a critical condition,” police spokeswoman Ambria Washington said. “The number could increase as the investigation is ongoing.”
Twenty-one people, including a police officer and a child, were taken to hospital and seven others were treated at the scene, according to the Times-Picayune.
The victims who were taken to hospital ranged from three to four years old up to 40-or-so years, the New Orleans Advocate reported.
Witness Kourtney McKinnis, 20, told the Advocate that the driver of the vehicle seemed unaware of what he had done. “He was just kind of out of it.”
The crowd was watching the Krewe of Endymion parade in the Mid-City section of New Orleans, a part of the city’s Mardi Gras celebrations.
New Orlean’s “Krewes” are the private organisations that lead parades and throw balls during the city’s Carnival season.
Video footage from the scene showed pandemonium immediately following the early evening incident, but the Krewe of Endymion parade, the largest and most popular of numerous Mardi Gras season parades in New Orleans, continued with little or no interruption.
The Federal Bureau of Investigation in New Orleans said its agents were “co-ordinating with our federal, state and local law enforcement partners to determine whether a federal violation has occurred”.
“It’s very hard to protect against somebody that’s very intoxicated that runs through a crowd,” mayor Landrieu told reporters, adding that barricades had been put in place. “People have to be responsible and they have to be thoughtful about what they do.”
Earlier in the day a man was wounded after a gun went off near the Krewe of Tucks parade elsewhere in town.
Police believe the weapon was accidentally discharged inside a portable toilet, according to the Times-Picayune.
“In both instances our officers were on the scene within seconds if not minutes,” Landrieu said.
