The situation was creating two classes in society, he said.
"What we're looking at now is essentially this landed gentry - if you've got mummy or daddy who own houses, you're likely to own houses," Mr Eaqub said.
"We're seeing this already in Auckland, where if you want to buy a house you really need help from somebody who's been in the market for a very long time.
"We're creating two New Zealands - this landed gentry, this wealth-generated, hereditary sort of wealth, those are the people who will be able to buy houses, and then there is the rest.
"We are creating this social and housing apartheid where you've got these people who are the 'generation rent' and they're locked out of so much of New Zealand that's predicated itself on owning a home."
He added: "Housing apartheid is, I think, this concept that 'generation rent' simply cannot participate in so much of how New Zealand is set up."
Mr Eaqub also claimed there was a "growing wedge" between the two classes, and that an increasing "ghettoisation" along ethnic and racial lines was emerging in New Zealand cities.
"We're pushing poor people further out, away from transport and amenities, and that's going to intensify."
The crisis risked destroying the core values of New Zealand society, Mr Eaqub said.
"That describes a New Zealand to me where your chance of success in life depends on whether your parents own their own home or not, rather than whether you have talent and whether you're applying yourself," he said.
"That can't be the New Zealand that we aim for, that can't be the New Zealand that's us, because that egalitarian story, that fair go, that equal opportunities story for New Zealand, which is so strong in our fabric, we're going to sacrifice that."