Blue John is only found beneath Treak Cliff Hill, near Castleton, and gets its name from its distinctive colour.
It is now only mined in two caverns, external – Treak Cliff Cavern and Blue John Cavern.
The stone was fashionable during the Regency period in the early 1800s and is displayed at Buckingham Palace and Chatsworth House.
Officers said: “The site is Site of Special Scientific Interest (SSSI) protected and quarrying of Blue John is strictly controlled.
“Theft of this rare fluorite not only harms the natural environment of the site and local economy, but it also harms the site’s heritage.
“It is sometimes said that Blue John was first discovered by the Romans.”
Police added the items would be assessed by an expert to determine their value.
