New Orleans Police Superintendent Michael Harrison told NBC station WDSU that the shootings, which occurred shortly before 7 pm (6:30 am IST), may be gang-related.
Witnesses told the local television station WWL that at least two gunmen were shooting into the crowd.
The Times-Picayune newspaper quoted witnesses as saying they saw several people lying on the sidewalk after the shooting.
Several ambulances were seen leaving the scene and 10 of the victims were taken to University Medical Center in New Orleans, WWL said. Police said others had been taken to hospital by private vehicles.
Media reports said it was not clear how serious the wounds were, or what started the shooting.
It is understood that there were two groups of people at the park -- a group who had walked there in a neighbourhood parade and a separate group watching or participating in a video.
According to FrenchQuarter.com, second line parades are "the descendants of the New Orleans' famous jazz funerals and, apart from a casket, mourners and a cemetery visit, they carry many of the same traditions with them as they march down the streets." There are dozens of second line parades scheduled throughout the year and throughout the city, usually on Sunday afternoons, according to the website. They range in size, level of organization and traditions.