The show's producer had to step in and apologise after broadcasting a "light-hearted" joke by Jeremy Clarkson.
The episode, filmed in Burma and Thailand and shown in March, featured a scene where the 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 was an example of "casual racism" and "gross misconduct".
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.