The three-week-old Welsh Mule and Texel Suffolk cross lambs were taken some time between midnight and 6am on Thursday 28 March.
Officers believe the person, or people, responsible would have had to have used a vehicle to transport the lambs from the field.
Sadly two lambs were found dead as a result of the theft.
PC Steve Rogerson from the CountryWatch team said: “Understandably the farmer is very concerned for the welfare of these animals.
“There is a possibility that the ewes could suffer and even die, and other lambs in the field could die as a result of shock.
“Those that were stolen are at risk of losing their lives in transit, or from being away from their mothers and not being kept in the right environment.
“This theft will come at a huge financial cost to the farmer, but this incident is all the more distressing for the victim as he has lambed these animals himself and raised the young ones from birth.
“It is very rare for something like this to happen in Hampshire, and we are asking our rural communities to spread the word so we can find these animals and ensure their safety.
“Do you know someone who may have come into the possession of these animals, or a farm that has had a sudden and unexpected influx of lambs?
‘I would urge anybody who can help our investigation to come forward.”
Hampshire NFU Adviser Sandra Nichols said: “We have been appalled at this theft as there are serious animal welfare implications for both the ewes and lambs.
“Anyone who has information should contact police and we also ask people to keep their eyes open, in case these animals should turn up somewhere.
“Please report any suspicious activity to police on 101. We have also been reminding our farmer members to check their roadside gates are secure.”
Anyone with information is asked to contact the CountryWatch team on 101, quoting 44190107152.
Alternatively you can call the charity Crimestoppers anonymously on 0800 555 111.