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.
More £40,000 of lead has been stolen from a 13th Century church with links to the family of the late Princess Diana.