The stock loss is estimated at up to $75,000.
"It's a possibility that these sheep were startled by someone wasn't supposed to be on the property," Detective Sergeant Greg Baird.
Poaching is becoming increasingly common around Southland and police want to hear from any farmers who see suspicious activity including vehicles or people who may not be normally seen around the neighbourhood.
"In this case we're particularly interested in anyone who might have seen suspicious activity in the area of Mt Wendon between 11pm on 2 February and 7am on 3 February."
Detective Sergeant Baird said police take poaching offences seriously.
The latest incident is on the back of an ongoing inquiry into illegal spotlighting on Department of Conservation land at Piano Flat.
