The 90-minute India special showed Clarkson talking to locals while his trousers were in a trouser press.
The episode also showed a car with a toilet in the boot, with the controversial TV presenter saying it was “perfect for India because everyone who comes here gets the trots”.
They also put banners on trains saying: “British IT is good for your company” and “Eat English muffins” which ripped when the trains moved to reveal an obscene image.
Raja Sekhar from the Indian High Commission in London said a letter was sent to the BBC to “convey our strong disappointment”.
The Commission said it had written the letter after being contacted by “too many people” who were “very upset” by the programme.
Sekhar added: “We were very actively helping out facilitating the visit but they ran down the whole society, culture and people. It’s really disgusting.
“We have a very close relationship with and respect for the BBC. The BBC is probably more admired in India than in England so we feel a bit let down.”
A BBC spokeswoman said: “We have received a letter from the Indian High Commission and will respond to them in due course.”
The BBC received 188 complaints about the show.
Last month the BBC had to apologise after Clarkson told viewers on live TV that workers on strike should be shot in front of their families.
They also had to apologise earlier last year to Mexico, when Clarkson’s co-presenter Richard Hammond made an insulting parody of Mexicans to describe a sports car.