The event has been put off until next year, with organisers citing "time constraints" as the main reason for the cancellation.
"Unfortunately, we had delays and time became too tight to do the build and the shows properly," said Campbell Smith, chairman of the New Zealand Music Foundation.
"It is disappointing to postpone this because ticket sales were strong and the artists still all committed."
Music veteran McGlashan said he expected the Big Band Build to be rescheduled for next year.
"It would have been a pity to sell it short but it will happen later on down the track," he added. "It will be a great event."
Conrad LaPointe, resource manager for Habitat for Humanity, is disappointed but insists no one will miss out.
"The house will still be built later this year, but at our premises at Otara instead of at the cathedral," he said. "It will go to a low-income partner family chosen from our records."
Ticket refunds are available from the original point of purchase, at www.nztix.co.nz and at www.ticketmaster.co.nz