He is described as European, 182cm in height, clean shaven, of medium to solid build and with short, dark hair.
Police, including members of the armed offenders squad, visited a property on the Lumsden-Riversdale Highway in the township of Balfour on Monday looking for him.
Detective Sergeant Mark McCloy, of Invercargill, said Shillito could be anywhere in the South Island and police were keen to find him.
He was not believed to be a danger to the public but anyone who saw him should not approach him, but call 111 immediately.
Anyone who had information about his whereabouts should contact their nearest police station or provide information anonymously via CrimeStoppers on 0800 555-111.