The regulator decided the use of the term "slope" by the controversial star, during the programme's Burma special screened in March, was offensive.
The ruling comes just three months after Mr Clarkson was caught up in another racism row which prompted him to apologise and he was given a final warning about his behaviour by the BBC.
In that incident unaired footage from the programme came to light in which he appeared to use the n-word.
Today's ruling by Ofcom involved a scene in which the presenters were involved in the construction of a bridge over the River Kwai and viewers saw an Asian man walking on the bamboo crossing, while Mr Clarkson said: "That is a proud moment - but there is a slope on it." Two viewers were concerned that the word "slope" was an offensive racist term.
An Ofcom spokesman said: "Ofcom has found the BBC breached broadcasting rules by including an offensive racial term in Top Gear, which was not justified by context.
"Jeremy Clarkson used the word 'slope' to refer both to an Asian man crossing a bridge, and the incline of the bridge. This was scripted in advance. The BBC failed to take the opportunity, during filming or post-production, to check whether the word had the potential to offend viewers."
The programme's executive producer, Andy Wilman, had previously apologised for the use of the term, saying it had been intended as a "light-hearted word-play joke" and that the team had been unaware the term was considered offensive.
A BBC spokesman said: "The programme apologised at the time and explained the context."
The motoring show has faced several controversies over the years, including complaints from Indian and Mexican politicians over remarks made about their countries while filming on location.