The Britain's Got Talent judge spilled the beans on her Heart radio show when comedian Carr went on to talk about their Amanda & Alan’s Italian Job, which sees them renovating a dilapidated home in Sicily.
Carr, 46, had pointed out to Holden that "no-one's really talked about you getting arrested".
"Oh yeah," said Holden, as her co-star Jamie Theakston exclaimed: "What?"
Holden then explained that there was a "police incident" but she didn't say what they were stopped for, just teasing: "But you have to watch that."
Carr said it was a hilarious moment, and 51-year-old Holden agreed: "It's so funny.
"We were pulled over by the police."
Theakston chimed in: "You didn't tell me you'd been arrested!"
"Well, yeah," said Holden. "There's a whole show there! They were pretty mean until I, we, turned on the charm."
Laughing, Carr exclaimed: "We turned on the charm!
"She turned into Mae West, 'Hey, that’s a lovely buckle on your trousers!'"
"I said, 'I love your belt buckle'," Holden laughed. "And then I was like, 'What's the Italian for belt buckle?!'"
The new TV show will see Holden and Carr turning a rundown property on the stunning island into a luxurious home.
The stars will be drafting in local tradespeople to show them the ropes.
But they will also be carrying out a lot of the work, like plastering and painting, themselves
Watch: Amanda Holden praises David Beckham for queueing to see the Queen