The protected monument was reportedly targeted between 4pm yesterday and 8am today.
Police said a window on a nearby outbuilding had also been damaged.
The would like to speak to anyone who either saw what happened or has any information about it.
The bronze statue, including the plinth, is more than 20ft high. It portrays Queen Victoria in Imperial regalia holding an orb and sceptre. It was erected in 1900 to commemorate her Diamond Jubilee.
Anyone with information is asked to call 01481 222222, ask for the sergeant’s office and give the reference OC2400002829 or Crimestoppers, anonymously on 0800 555 111.
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