The Community of St John the Divine were used by BBC bosses as templates for characters in the programme which follows a group of nuns delivering babies in post-war London.
The five sisters moved from London to Birmingham in the 1970s when faced with a massive increase in rent but are now being forced to move again.
Faced with a bill of around £17,500 to fix a leaking roof the sisters and a chimney they say they're devastated with the decision but have no choice.
At one point in the mid-1800s the Community had a large number of sisters working alongside Florence Nightingale in the Crimean war
Sister Christine Hoverd, 75, told The Guardian: "We prioritise and economise very carefully and try to keep the building in a good state of repair. But the roof was the straw that broke the camel's back.
"We just don't have that sort of money [for repairs]. We realised we have been sailing very close to the wind."
Sister Margaret-Angela King, 79, told the newspaper: "It's so expensive to run. We're run off our feet, deadbeat tired. We had to be realistic".
The convent includes 20 bedrooms and a chapel. It has been valued between £800,000 and £900,000.
The nuns say they want to sell to another religious group and do not wish to see the building demolished and the land used for development.
Enough money has to be raised through the sale to let the sisters buy a new home.
Currently the group survives on pensions, donations and the small returns on a few longstanding investments.
The nuns say they still receive calls from TV bosses for advice whilst they film Call the Midwife.