The Pedigree Shropshire ewe lambs were taken by thieves from Forge Mill Farm in West Bromwich on the evening of Sunday, July 25.
Farm staff have been left "devastated by this callous act", said Sandwell Council deputy leader Maria Crompton, who has warned people that the lambs are "not fit for human consumption".
The lambs were due to join the farm's breeding flock next year, as part of a programme with the Rare Breeds Survival Trust, which aims to boost numbers of vulnerable livestock in the UK.
Sandwell Council has passed on CCTV of the incident taking place to West Midlands Police, which is investigating the animal thefts.
Councillor Crompton, cabinet member for the borough’s farms and parks, said: "This theft is a huge loss for the team that works so hard to care for the animals throughout the year and for the people of Sandwell that visit our farm.
"The farm staff are devastated by this callous act. These lambs are irreplaceable as it takes a huge amount of time and energy to produce rare breed sheep of such high genetic quality as these and for them to be stolen, and most likely slaughtered, is disgusting.
"We are appealing for anyone who witnessed people acting suspiciously on Forge Lane, West Bromwich around 10.30pm on Sunday, July 25 or knows anything to call the police.
"The animals taken from Forge Mill Farm are not fit for human consumption. Don’t buy meat except from a reputable shop – it could be a health risk, not a bargain."
Anyone with information is asked to contact West Midlands Police, quoting crime reference number 20/146 4767/12 and incident report number 849 26/07/2021.
Sandwell Council says any cases of illegal slaughter should be reported to its consumer protection team at EHTS_Enquiries@sandwell.gov.uk.