Scenes in which Top Gear presenters Jeremy Clarkson, Richard Hammond and James May poked fun at Mexicans will be cut before the show is broadcast in the United States next week.
The Mexican ambassador complained to the BBC about the "outrageous, vulgar and inexcusable insults" made on the show after Richard joked that Mexican cars reflected national characteristics, saying they were "just going to be lazy, feckless, flatulent".
Also in the show, James described Mexican food as "like sick with cheese on it" and Jeremy predicted they would not get any complaints about the show because "at the Mexican embassy, the ambassador is going to be sitting there with a remote control like this (snores). They won't complain, it's fine".
The corporation wrote to His Excellency Eduardo Medina-Mora Icaza to say it was sorry if the programme, broadcast on January 30, caused offence.
But it claimed national stereotyping was part of British humour and the remarks were akin to labelling Italians as disorganised and over-dramatic, the French as arrogant and the Germans as over-organised.
A BBC spokeswoman said: "Top Gear episodes are routinely edited for international transmission, both to fit broadcasters' time slots and for rights reasons."
The show also came under fire from comedian Steve Coogan who said the trio were guilty of "casual racism".
The show is broadcast on the BBC America channel and a US version of the show recently began on The History Channel.