Jack the Limeworker is very popular with local families said the owners of the woods, Buxton Civic Association (BCA).
"We are really sad to report that our very popular sculpture of 'Jack' the lime worker in Grinlow Wood has been vandalised with graffiti carved into him,” said a spokesperson for BCA.
“The fact that the vandalism included anti-semitic content raises this from stupid vandalism to horrific hate crime. Whoever is responsible should think very hard about the deep hurt and revulsion he or she has caused.
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“This is so sad because Jack was in memory of all the families who had worked so hard on that hillside during the 18th & 19th centuries, many of whom had made their simple homes in the lime spoil.
“He was also incredibly popular with families and children, many of whom posed for photos on his knee."
The spokesperson added: “We are investigating what we can do to repair him. Meanwhile we will probably have to cover him.”