Taranaki-based drag Queens Erika and CoCo Flash were set to tour the country with their show aimed at children of all ages, to coincide with the Out on the Shelves rainbow reading campaign month in June.
Last month, protests by Destiny Church forced the cancellation of their Rainbow Storytime events in Hastings and Rotorua.
On Facebook, organisers of the event said they have been forced to cancel the New Zealand tour, as well as several other planned drag productions, due to threats they have received.
One post said promises of violence had also forced one of the event's stars, Erika Flash, to relocate to the UK.