The ewes were taken from Forge Mill Farm in West Bromwich during the night of October 24 and were believed to be carrying twins.
The farm has been targeted by thieves in the past with two rare breed lambs stolen earlier in the year.
Alex Dunn, farm manager at Forge Mill farm said: "This is a devastating loss to the farm and to the people of Sandwell, after all these are their sheep.
“We are here to serve the public and to provide experiences and educate about food and farming.”
It is feared the thefts are related to a rise in the trade of illegal meat despite the fact the ewes taken are not fit for human consumption.
Alex added: “It is heartbreaking to think that some of the same people we serve might also be responsible for stealing and slaughtering these sheep in such an inhumane manner.
"It is a really big public health issue as they are not fit for human consumption.
“We need people to be aware if they are offered meat outside of a normal situation, they need to be asking questions, a bargain isn't a good thing and it might be illegal.”
Farmers and staff are also concerned for the welfare of the remaining sheep and fear that the ewes may have lost or will lose their lambs due to the stress of the incident.
The farm has fitted extra security cameras, hired extra security and is even looking into new technology to track and trace any animals that go missing through GPS.
This loss will mean that the farm will have 10 to 20 per cent fewer lambs for visitors to enjoy this year.
Sandwell Council’s cabinet member for culture and tourism Councillor Danny Millard said: “This is a callous, inhumane and criminal act, this kind of selfish behaviour will not be tolerated and I urge anyone that has information to contact the police.”
Investigations are still ongoing and anyone with information is urged to call 101 and quote the crime number 20/183 0794/21.