Regulator Ofcom said that Clarkson's use of the word "slope", as slang for a person of Asian origin, was potentially offensive and that the BBC had failed in its duty to viewers by broadcasting it.
The ruling comes just three months after Clarkson was forced to apologise over footage in which he appeared to use another racist term as part of an old nursery rhyme during filming of Top Gear.
The show has previously got into hot water over its depictions of Mexicans, Albanians, Romanians and Germans.