Lavea hurt his hamstring in a club rugby match at the weekend and the seriousness of the injury has now been confirmed by New Zealand Rugby Union medical staff.
Hawke's Bay's Matthew Berquist has stepped into the tour party in his place.
New Zealand Maori coach Donny Stevenson said: "Tasesa was excited about being part of the team for the first time and he is understandably disappointed that he had to withdraw.
"But this is an opportunity for Matt to step up to this level and I have full confidence that he has the ability to do that."
The Maori face New South Wales Waratahs in Sydney before flying to the Churchill Cup tournament in the North America.