Around 20 tonnes of metal was taken from the 14th century All Saints Church in Houghton Conquest, Bedfordshire.
The theft was discovered on Tuesday when one of the cleaners noticed daylight coming through the roof.
Gary Mudd, chairman of the church council, posted photographs online showing the damage done to the Grade I listed building.
It is feared that the cost of replacing the lead could be as high as £100,000.
His wife Helen Mudd, also a church member, said: "It's just sheer greed isn't it?
"The cost of the repair is going to be absolutely astronomic.
"It's a Grade I listed building so we have to use like-for-like materials and whatever we repair it with, it's not going to be cheap.
"Fundraising just can't keep up with the demands of a building like that.
"It's an historical building and it's wanted and loved by the community, whether they're religious or not.
"A small community like this isn't going to be able to raise the funds in five minutes."
Police said the thieves may have posed as workmen and carried out the theft over a "prolonged period of time".
Inspector Nick Masters described the theft as "audacious" and asked any residents with CCTV to check their footage.
"We suspect the people responsible may have been going backwards and forwards to the church for a prolonged period of time," he added.
"Due to the sheer quantity of lead taken, it's unlikely that it happened over a few days.
"It's likely that the people responsible were driving trucks or vans so they could transport scaffolding or ladders in order to access the roof of the church, and may have posed as tradesmen.
"Therefore, we're asking anyone who has seen anything suspicious in the area over the past few weeks to get in touch."
Bedfordshire Police have appealed for anyone who saw anything suspicious to come forward.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
