On Monday morning's show, Henry read from a magazine article about the Scottish singer, laughing as he described how she was "starved of oxygen" at birth and suffered an intellectual disability, The Dominion Post reported.
"Here's the really interesting revelation: she is in fact retarded ...
"And if you look at her carefully, you can make it out," he said.
IHC New Zealand spokeswoman Philippa Sellens said it was "highly offensive" that Henry referred to Boyle as retarded.
"It was in extremely bad taste to use his position as a broadcaster to 'entertain' by mocking a sector of the community that has difficulty speaking up for themselves."
IHC had had "a massive response" and was encouraging the public to complain to TVNZ and the Human Rights Commission.
TVNZ spokeswoman Megan Richards said she was unable to comment on the complaints as they were "going through the usual process".
The Broadcasting Standards Authority found Henry had breached standards of good taste, decency and fairness after he read viewer comments that a female guest, Greenpeace worker Stephanie Mills, had a moustache. He then added his own comments, while his co-host Alison Mau pleaded with him to stop.
"That was a moustache on a lady," he said. "People can say what they see, it's television isn't it?"
