Police spokesman Tyler Gamble said officers were on their way to break up a big crowd at the city's Bunny Friend Park when shots were fired.
Ambulances took 10 people to hospital, Mr Gamble said, and others were taken by private vehicles.
It is yet not known what started the shooting or how severe the injuries are.
According to Mr Gamble, there were two groups at the park - one had walked there as part of a neighbourhood parade, while others were watching or participating in a video being made in the park.
Witnesses told local TV station WWL that there were about 500 people at the park and that two gunmen opened fire in the crowd.
At least 16 people have been wounded in an apparent shooting at a park in New Orleans, police say.