Hammond joked that Mexicans are "lazy, feckless [and] flatulent" on the motoring programme, which led to a complaint from the Ambassador and a statement from the BBC.
Lord Grade, the former head of ITV, told The Daily Telegraph: "I don’t think that’s acceptable in this day and age.
"That was disgraceful, it was horrible. How dare he [Richard Hammond] sit there, [on] prime-time television, casting aspersions on a whole nation.
"What's he going to do next, talk about the Jews making money? Or the slitty-eyed Chinese, like the Duke of Edinburgh? I'm not a PC fascist, but it seemed to me to take us back to the dark ages of television."
However, Grade defended the corporation regarding the recent ageism row, which saw former Countryfile presenter Miriam O'Reilly win a tribunal case after being dropped by bosses.
On the subject, the broadcaster stated: "I think that's nonsense. You've got to be free. Anything that constrains the editorial chiefs having the ability to pick and choose and exercise their professional judgment about who's right for the show is a detrimental backward step.
"If what was said to have been said to [O'Reilly] was true - about Botox and the rest of it - that was absolutely unacceptable. And she was quite right."