The band released a statement to their "great fans in Australia and New Zealand".
"Unfortunately we need to postpone our upcoming tour so that we can put the finishing touches on our new album. We can't wait to see you in November/December. "Until then, much love, BHIC." Mr Holley said he was hopeful they would be able to find an alternative band, and they had several lines of inquiry open.
"If we could find an artist with an alternative genre we would, but it is artist driven.
"We enjoy hosting artists and annual events, and creating great opportunities for people. Patrons know we have a record of producing good events ... this is only our second cancellation ever."
Call It What It Is will be Ben Harper and the Innocent Criminal's first album in eight years, and was due for release in April 2016 on Stax Records.
On their New Zealand tour, Kiwi audiences were to be among the first to hear new songs from the album.
Tickets for the show will be valid for the rescheduled date without the need to exchange.