Vandals have targeted the Roman hypocaust in St Albans which dates back 1,800 years.
Between 5.30pm on June 15 and 2.30pm on June 16, flint rocks were prised out of the decorative metal cages around the hypocaust building in Verulamium Park and thrown at the building's high windows.
Holes were smashed in the glass, which caused shards and debris to fall from the windows and land on the mosaic and exposed underfloor heating system.
This is the ancient remains of a reception room in a large town house built near Watling Street in AD 200.
There is no major damage to the historic floor and the building has been reopened to the public.
St Albans Museums staff discovered the damage on June 16 and reported it to Herts police, who are searching for the culprits.
Portfolio holder for community, leisure and sport at St Albans district council (SADC), Cllr Anthony Rowlands, said: "This is an appalling crime.
"It is very sad that someone or some people have targeted one of the district's most important museum and heritage sites in this way.
"This is an act of mindless vandalism and I would ask anyone who can help the police with their inquiries to do just that."
Both the mosaic and hypocaust were uncovered during excavations in the 1930s by archaeologists Sir Mortimer and Tessa Wheeler.
They were left preserved underground until 2004, when they uncovered, protected by a new building, and opened to the public for free. The hypocaust has been described as "a marvel of Roman engineering" and "an excellent example of the first indoor heating systems installed in Britain".
It allowed hot air to circulate beneath the floor and through the walls of buildings.
St Albans Ch Insp Lynda Coates said: "The hypocaust is a really important part of St Albans' history and we have a duty to protect it from mindless vandalism so future generations can enjoy it.
"It's very sad that a person or people have tried to damage it. We will do everything in our power to trace those responsible."
Anyone with information about the crime, or who saw people acting suspiciously by the hypocaust, should contact police on 101.
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