Fellow guest Rod Stewart looked uncharacteristically stony-faced at the gag, while Alex Jones, one of the hosts of the show, shook her head and grimaced.
Now two viewers have complained to communications regulator Ofcom, which is looking into whether the programme on November 4, broke television rules.
"We're investigating whether potentially discriminatory comments in this programme met generally accepted standards," a spokesman said.
Carr, who frequently appears on the BBC, will not be able to plead ignorance about broadcasting guidelines.
Before he launched into the controversial gag, he told presenters: "Don't play my stuff on your show, Ofcom will get involved."
He also admitted that his comedy routines have become much more foul-mouthed and "ruder" over the years.
It is unusual for Ofcom to launch an investigation against a broadcaster after only two complaints, prompting speculation among insiders that the watchdog wants to make an example of the incident.
It is not the first time Carr has grappled with bad publicity.
Three years ago, the comedian was one of a number of high-profile figures who was heavily criticised for using a tax avoidance scheme.
He later stopped investing in the set up and admitted that he had "made a terrible error of judgment".
The BBC declined to comment on The One Show incident, while Carr's spokesman could not be reached for comment.
- Daily Mail
