Peter Bainbridge made the comments while being interviewed on BBC Breakfast, sparking complaints from viewers.
He was being asked about the effectiveness of IQ tests at judging intelligence.
"So most IQ tests will have Mr and Mrs Average scoring 100 and the higher you get, the brighter you are. And if your IQ is somewhere around 60 then you are probably a carrot," Mr Bainbridge said.
After the interview with presenters Louise Minchin and Charlie Stayt, some of the complaints were read out on air. The hosts then apologised and read out a personal apology from Mr Bainbridge.
One viewer, an employee of learning disability charity Mencap, said she was "shocked" and "disgusted" by the comments.
Ciara Evans, who has a learning disability, urged Mr Bainbridge to "engage his brain before his mouth".
One of the complaints read out on air came from a Dr Sullivan, who said: "As a clinical psychologist who has worked with many people who have an IQ below 60, I find these comments to be offensive and completely incorrect.
"Such comments perpetuate the stigma around an individual with learning difficulties."
A BBC spokeswoman said: "A number of viewers contacted BBC Breakfast who were offended by comments made by a contributor during a live interview. Clearly, we do not condone the comments and sincerely apologise for the offence caused."