The current postmaster at Kinsley post office says he has been left with no choice but to leave.
Brian Enright said he was no longer earning enough money to run the post office on Wakefield Road, where he also lives.
Mr Enright, who bought the business 15 years ago, said he had been borrowing money from family members and had cashed in some of his pension early to help keep the post office running.
“I just can’t afford to stay open any more,” he said. “I have been subsidising the business.”
He added: “My shop is very small. Post offices like mine don’t have a retail side. When I bought it, it was simply as a post office.”
The Post Office Ltd is advertising for a retailer or business person with their own premises to integrate post office services into their company.
Any business which takes it on would get paid a fee for post office transactions including parcel collection, postage and travel money.
The advert, on runapostoffice.co.uk, estimates that fees for a Kinsley branch would be between £7,600 and £8,600 per year.
The Post Office said it is also looking for a new partner to run the current Fitzwilliam post office.
A spokesperson said: “The vast majority of our 11,600 branches are run by independent business people, including Kinsley and Fitzwilliam branches.
“We are working hard to find new partners to take on these branches as part of a thriving retail business.”