Last week, BBC director general Mark Thompson defended Clarkson after the Top Gear host had prompted outrage by saying on the BBC One show that workers taking industrial action should be "executed in front of their families".
Thompson told MPs on the Commons culture, media and sport select committee that Clarkson's comments were made "entirely in jest", and insisted that he would not be sacked over a "couple of flippant remarks", despite 32,000 people complaining to the BBC about the incident.
Ofcom has also received 763 complaints about Clarkson's appearance on the show, and so has decided to launch an investigation.
"Ofcom has taken the decision to investigate comments made by Jeremy Clarkson on BBC one's The One Show," said an Ofcom spokesman.
"We will make the outcome of the investigation known in due course."
Ofcom will now probe whether the remarks were in breach of rule 2.3 of the broadcasting code, which says that any potentially offensive material aired must be "justified by the context".
Clarkson's controversial comments ensured that the One Show episode aired earlier this month was Ofcom's third most complained about TV show of the year.
The programme was just behind Matthew Wright's ill-advised joke about a murder in Scotland on Channel 5's The Wright Stuff (2,220 complaints), and cutting remarks on ITV1's Dancing On Ice by judge Jason Gardiner (784 complaints).
> Bill Oddie slams BBC's handling of Jeremy Clarkson controversy