The clergyman, in his 50s, told nurses he had been hanging curtains when he fell backwards on to his kitchen table.
He happened to be nude at the time of the mishap, said the vicar, who insisted he had not been playing a sex game.
The vicar had to undergo a delicate operation to extract the vegetable, one of a range of odd items medics in Sheffield have had to remove from people's backsides or genitals.
Others include a can of deodorant, a cucumber, a Russian doll – and a carnation.
Speaking of the vicar, A & E* nurse Trudi Watson, of Sheffield's Northern General Hospital, said: "He explained to me, quite sincerely, he had been hanging curtains naked in the kitchen when he fell backwards on to the kitchen table and on to a potato.
"But it's not for me to question his story. He had to undergo surgery to have it removed."
She advised anyone tempted to use such objects in sex games to think again.
"It can be very dangerous and potentially life-threatening," she said.
"Surgery can lead to infection, nasty scarring, and it could possibly end up with the person having to use a colostomy bag as a result."
A hospital trust spokeswoman in Sheffield said: "Like all busy hospitals we do see some unusual accidents.
"But our staff deal with them in a discreet, professional and kind way."