The 66-year-old TV presenter said he discovered the animals were missing when he went to count his flock in Chadlington, Oxfordshire, with Clarkson's Farm co-star Kaleb Cooper, and told those responsible to "put them back" in an interview with The Sun.
Clarkson told The Sun: "The police have been very good, actually.
"Once you go through 700 hours of recorded messages, I got through to a girl.
"I said, 'I know it's going to sound like I'm from 1856, but I've had some sheep stolen'.
"She went through the name and address and then she said, 'oh, not your Easycares' (a British breed of sheep). She's obviously been watching the show, but it is the Easycares."
He added: "It's a farm. We're armed. Just so they know.
"It pisses me off. Honestly, it just pisses me off."
The former Top Gear presenter told The Sun that the sheep were worth more than 2000 pounds ($A3800) at market, and added that he was worried some in other fields of his farm may have also been stolen.
He claimed it had been done at night or during a day when the farm was not being filmed for Prime Video's Clarkson's Farm, when he said there was "a film crew here all the time" and "a drone in the air".
Asked whether he believed the show had made his farm a target, Clarkson said: "It's more likely to make you a target than less, but I still don't think they've been stolen because they're on Diddly Squat.
"How can you (stop it) if someone's determined to steal your livestock?
"This is 1000 acres, it's a big farm. Anyone could be anywhere and you wouldn't know."
The theft was reportedly raised with Thames Valley Police by Cooper and land manager Charlie Ireland.
National Farmers' Union president Tom Bradshaw said the theft of Clarkson's sheep "really hurts," adding that farmers were facing "a cash-flow and confidence crisis like we haven't seen in decades".
Bradshaw told Times Radio: "Those livestock have been cared for by that farmer, by Jeremy in this instance, for so long and it really hurts, because suddenly you have nothing to sell.
"I'm afraid it's highly likely that those sheep will have been slaughtered to go into the food chain."
Earlier this year, Clarkson revealed he had been diagnosed with "aggressive" prostate cancer, which had been discovered early, during an episode of Clarkson's Farm.
In a subsequent interview with The Sunday Times, Clarkson said that a PSA test in April showed no indication of cancer and he is in remission.
On Wednesday, Clarkson appeared at the premiere of the latest series of Prime Video motoring show The Grand Tour, in which three new presenters - Francis Bourgeois, Thomas Holland and James Englesman - will take over from him, James May and Richard Hammond.
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