Thieves stole about 12 tonnes of lead from the roof St Mary's Church, Great Brington, Northamptonshire, in the early hours of Tuesday morning.
They stripped more than 3,000 sq ft of lead from the church.
Princess Diana's father, the 8th Earl Spencer, is buried at the church, which also includes the Spencer Chapel.
The church is sited near the Princess's ancestral seat of Althorp, which was inherited by her brother Charles Spencer, 9th Earl Spencer, in 1992.
Northamptonshire Police said it was believed the thieves broke through a gate then drove a vehicle into the churchyard, knocking over a gravestone on the way.
Officers investigating the theft have asked anyone who was in the area at the time or who knows anything about the theft to contact police.
Rev Sue Kipling, rector of the Spencer benefice - which includes the church of St Mary the Virgin with St John in Great Brington - said: "It's a huge loss to us. It will cost more than £40,000 to replace.
"You can now see the sunlight coming into the church through the roof, although the Althorp estate has provided tarpaulin to protect the inside of the building in the short term."
She said the church held a service and prayed for the thieves.
The church is also connected to the first president of the US. George Washington's great-great-grandfather Lawrence Washington is buried in the chancel.

A BBC investigation reveals Southampton docks does not monitor its air pollution rates, despite the city being among the most polluted in the UK.
Southampton City Council estimates the port contributes up to 23 per cent of air pollution in the city.
Ships can use a "plug-in" system to reduce emissions but not in the UK.
It comes after the World Health Organisation (WHO) called Southampton one of the most polluted cities in the UK.
The city's port welcomes thousands of ships a year, including some of the biggest cruise liners and container ships in the world.
The vessels leave their engines running while docked to power their electrics, but elsewhere in the world ships use a shore-based electricity supply, virtually eliminating their emissions.
Cargo and cruise ships, including the Queen Mary 2 and Britannia which regularly dock in Southampton, use the method - just not when visiting the British port.
Port Director Alastair Welch from ABP said: "The challenge has been in particular there is no one standard for shore power. I'd like it in place as soon as possible.
"I should emphasise shore power is not the only answer and that's why we're working with solar power and hybrid ships now, because all of them have a part to play for the future."
A review of Air Quality in Southampton in 2015 by the local authority showed the port is believed to contribute between seven and 23 per cent of the air pollution, while cars contribute 18 per cent and HGVs 12 per cent.
The government has since told Southampton to implement clean air zones by 2020 and the council is implementing a Clean Air Strategy to meet national goals.
More £40,000 of lead has been stolen from a 13th Century church with links to the family of the late Princess Diana.
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Southampton, the biggest cruise port in Britain, has no way of monitoring air pollution generated by emissions from the largest ships in the world.