The Daily Record reports that the Ambassador wrote to the corporation after Sunday evening's episode of the show.
In the instalment, hosts Jeremy Clarkson, Richard Hammond and James May were reviewing a Mexican sports car.
Hammond suggested that cars reflect national characteristics, adding that Mexican vehicles would be "lazy, feckless, flatulent, leaning against a fence asleep looking at a cactus with a blanket with a hole in the middle on as a coat".
The trio also made fun of Mexican food, with Clarkson describing it as "refried sick" and May saying it is "like sick with cheese on it". Clarkson also suggested that they would not get any complaints because the Ambassador would be asleep.
In a letter to the BBC, the Ambassador wrote: "The presenters of the programme resorted to outrageous, vulgar and inexcusable insults to stir bigoted feelings about the Mexican people, their culture as well as their official representative in the United Kingdom... These offensive, xenophobic and humiliating remarks only serve to reinforce negative stereotypes and perpetuate prejudice against Mexico and its people."
A spokesperson for the BBC said: "We have received a letter from the Mexican Ambassador and shall respond to him directly."
The news comes shortly after the Japanese Embassy complained to the BBC about an edition of QI which included jokes about a man who survived two atomic bombs.