The show's producer had to step in and apologise after broadcasting a "light-hearted" joke by Jeremy Clarkson that lead to the complaint of racism.
The episode, filmed in Burma and Thailand and shown in March, featured a scene where the motoring show's stars built a bridge over the River Kwai and as an Asian man walked over it Clarkson said: "That is a proud moment, but there's a slope on it."
The Ofcom investigation will look at whether the clip counted as a breach of "content standards".
Somi Guha, an actress who complained to the BBC, said the language used was an example of "casual racism" and "gross misconduct".
It comes after a troubled few weeks for the show and its most famous presenter who is reportedly getting divorced from his wife after 21 years of marriage.
Clarkson was embroiled in controversy last week when it was claimed he used the N-word while reciting the nursery rhyme Eeny, Meeny, Miny Moe during filming of BBC2's Top Gear.
The Daily Mirror saw unaired footage of him using the nursery rhyme to compare two sports cars and claims the word "n*****" can be heard.
Clarkson said he "mumbled where the offensive word would normally occur" in two takes, and used the word "teacher" in its place in a third.
He later apologised and said the BBC had given him a final warning about his behaviour.