The group was due to play an open-air concert with headline act Eminem on Saturday in Auckland.
Border Operations Manager Karen Urwin said Thursday that authorities decided to decline visas to six group members after becoming aware of a 2011 incident in Boston in which some witnesses accused the group of inciting fans to attack police officers.
Group member Tyler, The Creator vented his frustration on Twitter on Thursday.
"They said we were 'terrorist threats and bad for the society' or whatever. Sick," he wrote. He later tweeted, "I love NZ tho."
The group is also known as Odd Future Wolf Gang Kill Them All.