Senior Constable Murray Hewitson, of Owaka, said the Wapiti-cross stag was in a paddock with other deer when it was slaughtered some time before 2am.
The stag was gutted, the carcass removed, with some internal organs left behind.
He said it appeared a vehicle had been backed up to the deer fence, and the gate opened to remove the dead stag.
Snr Const Hewitson said more than one person would have been needed to lift the stag.
The paddock is beside Puketiro Rd, about 15km south of Owaka. The stag had been on the farm for more than seven years and was used as a stud, Snr Const Hewitson said.
''A real hunter would know that it was farmed ... the meat wouldn't be that great.''
He would like to hear from anyone who saw anything suspicious in the area, or who might have heard anyone bragging about shooting a stag with a good head.
Poaching was an ongoing problem in certain areas of Otago, he said.
Anyone with information is asked to contact Snr Const Hewitson at the Owaka police station (03) 419-1070.
