The graffiti has been daubed on the former Skaw radar station on the isle of Unst and has defaced a World War II scheduled monument site – a title given to the country’s “most significant sites and monuments”.
It is understood that the paint makes reference to the point being the most northerly graffiti spot in Britain.
A spokesperson for Historic Environment Scotland said any alterations to scheduled monuments – including the application of paint – require consent.
The Historic Environment Scotland spokesperson said: “It is an offence to undertake works without consent and we will investigate in line with our enforcement policy.”
It is understood HSE are investigating the vandalism.
Police Scotland said it had not received any recent reports of graffiti on the historic structure.