The group was due to play an open-air concert with headline act Eminem on Saturday in Auckland.
Border Operations Manager Karen Urwin said authorities decided to decline visas to six of the rappers after becoming aware of a 2011 incident in Boston in which some witnesses claimed group members incited fans to attack police officers.
"It's not a decision we take lightly and not one that happens often," Urwin said.
Lead group member Tyler, The Creator vented his frustration on Twitter on Thursday:
The hip-hop group, which is also known as Odd Future Wolf Gang Kill Them All, is known for its anarchic style and lyrics that canvas drugs, killing and rape.
Urwin said the six rappers had intended to stay in New Zealand just a few days before leaving for Australia.
She said it was rare to ban musicians under rules that cover character concerns. She said those provisions in the past have been used to stop people like white supremacist group leaders and high-profile Holocaust deniers.
She said some people wrongly assumed authorities considered the group's lyrics in imposing the ban.
"If we banned people who used swear words, we wouldn't have many people left in New Zealand," she said.
In an official statement, Immigration New Zealand said: "Odd Future has been deemed to be a potential threat to public order and the public interest for several reasons, including incidents at past performances in which they have incited violence."
In the 2011 incident, Tyler, The Creator was signing autographs at a comic store when police were called because of the large number of fans. News reports at the time said some people climbed on the roof and shouted insults at the police, and some viewed that as inciting fans to attack.
Tyler, The Creator had been arrested and charged with vandalism at a West Hollywood, Calif., night club in December 2011. It is unclear if that arrest also played a role in the rapper's visa request denial.
Urwin said an Odd Future group member in Australia tweeted details of a woman campaigning to have the group banned, which resulted in her receiving threats.
In 2012, New Zealand banned former heavyweight boxing champion and convicted rapist Mike Tyson from coming to a speaking engagement due to his criminal history. Last year it banned musician David Rovics, citing his blog posts on drug-taking and a Canadian ban for giving false information to immigration officials there.