The theft took place from a property on Orr Road, Murchison, between November 1 and November 18 this year.
Police believe a stock truck was likely to have been used in the theft of the sheep.
The owner said the sheep stolen were the pure bred breeding ewes from the flock.
A number of other sheep on the property were left behind.
The Damara breed is a meat breed that sheds its wool and does not require shearing.
Anyone having information are requested to contact LSC KEAST at Murchison Police on 5826 2222 or Detective LSC WREN at Shepparton CIU 5820 5777 or Crime Stoppers 1800 333 000.