Those wounded by the eruption of gunfire in the early afternoon attack included 17 adults and two 10-year-olds, the local police department said in a statement.
"Many of the victims were grazed (some by bullets that ricocheted)," it said. "At this point, there are no fatalities, and most of the wounds are not life-threatening."
The injured children - a boy and a girl - suffered graze wounds and were in good condition while a man and a woman were still in surgery late Sunday.
The Federal Bureau of Investigation said the shooting was unrelated to terrorism, calling it "street violence."
"From all of our intelligence, we have no reason to believe it was an act of terror, just street violence," Mary Beth Romig, a spokeswoman for the FBI in New Orleans, told AFP. But "certainly today was not a normal day in New Orleans."
The incident comes less than a month after twin bomb blasts at the Boston Marathon killed three people and wounded more than 260. In December, a gunman opened fire at an elementary school in Connecticut, killing 20 children and six staff members.
New Orleans Police Department Superintendent Ronal Serpas told reporters earlier that shots from "maybe two different types of weapons" rang out and that police saw three people running away immediately after the shooting.
"It appears that these two or three people just for a reason unknown to us, started shooting at, toward or in the crowd," Serpas said. "It was over in just a couple seconds."
Police were searching for a motive for the shooting and appealed to the public to come forward with any clues. A $2,500 cash reward has been offered to information leading to the arrest and indictment of those responsible.
"It's just a very tragic day for us," New Orleans Mayor Mitch Landrieu told reporters after visiting some of the wounded in hospital.
"We will find them," he vowed, also urging members of the public to step forward "so that we can find people who do this and make sure that they don't hurt innocent victims anymore."
He also called for a reduction of crime on the streets of the city known as the Big Easy.
"The specialness of the day doesn't seem to interrupt the relentless drumbeat of violence that I have talked about so much on the streets of New Orleans," he said. "It's a shame and it's got to stop."
"It is important for us... to change the culture of death on the streets of New Orleans to a culture of life."
The Times-Picayune newspaper quoted Serpas as saying there were about 300 to 400 people in the parade and some 200 people in the area of the shooting.
The newspaper reported that one of its journalists, who was participating in the parade, heard six or seven shots being fired.
It also cited a parade participant as saying that those in the event were throwing teddy bears and candy to watching revelers.
"I think what frustrates all of us is the selfishness of some people, and I think what frustrates all of us is that the great culture of this city sometimes stumbles a bit because of the selfish behavior of some people," Serpas told reporters.