The flight was delayed while airline staff located an aisle chair so Ms Black could be shifted back two rows.
The woman did not ask the two teenage boys, who were seated next to her in the front row, to move in her place.
"My colleague and I were quite gobsmacked, really, that somebody could be so callous and uncaring - believe that their Gold Elite status gave them the right to treat somebody with a disability with such disdain," Ms Black said.
She had travelled extensively for her work - making television programmes about how disabled people face challenges - and had never experienced such discrimination.
"I've heard stories of discrimination all over but I have never experienced, or even heard of anyone experiencing, something so blatantly ignorant and rude," she said.
"I felt humiliated. For anybody with a disability to be humiliated, I just, you know, it destroyed my faith in humanity for the day."
Airline staff pleaded with the woman - who Ms Black described as a "well turned out" 40-something blonde - to change her mind.
"I saw the air hostess lean in and I know she would have been telling her that I am disabled and they didn't have an aisle chair. This woman said 'I don't care'."
Ms Black also heard the woman mention her Gold Elite status.
"I don't know who she was," Ms Black said.
"She seemed to think she was somebody. All that time she just stood there. The air hostess asked her a couple of times to reconsider because it was delaying the flight. She was like 'nope'.
"I was just so embarrassed. I felt sorry for her kids, actually."
The fact she was travelling to Wellington for meetings about the TVNZ-screened programme Attitude, which chronicles the challenges faced by disabled people, was ironic, Ms Black said.
"Our whole thing is by showing how disabled people are getting out there and living their lives we can change perceptions around disabled people."
Air New Zealand said via a statement it was satisfied its staff did all they could to "accommodate the needs of both customers".
The airline confirmed the flight was delayed by eight minutes because of a boarding issue and getting Ms Black seated.
On rare occasions because of operational issues the airline would ask passengers to give up their allocated seats, it said.
There was no issue with the availability of aisle chairs and the problem experienced on flight NZ247 did not occur often.
Air New Zealand Airpoints members reach Gold Elite status when they accumulate 1500 status points, which are awarded each time a passenger flies.