Countrywatch officers are urging dog owners to ensure they keep their pets under control.
Between 3pm on Saturday, February 16 and 8am on Monday, February 18, three sheep were left injured in West Hoe Lane, Bishops Waltham.
The sheep are believed to have been attacked by a dog. One of the sheep has had to be destroyed because of the injuries sustained.
This comes less than three weeks after a similar incident in Clanfield on Thursday, January 31 where it was unknown if a pregnant sheep would survive after suffering a bite wound to her face.
PC Jon Radcliffe from the Hampshire Constabulary Countrywatch team said: "This sort of incident causes horrific injuries to the animals involved and should act as a stark reminder as to why there is legislation in place outlining that dog owners must keep their animal under close control.
"Even the most well behaved dog can revert to instinct when near livestock potentially causing distress, injury and loss of life.
"If a dog worries livestock, the dog owner or the person responsible for the dog at the time is guilty of an offence under the Dogs Act 1953 and may be sued for compensation by the farmer.
"Land owners have the right, as a last resort, to shoot any dog worrying their livestock - so these owners are also putting their beloved pet at unnecessary risk.
"These types of incidents are distressing to both the animals and the farmer with loss of livestock and income.
"We by no means want to stop dog walkers from enjoying the beautiful countryside our county has to offer but we do want to remind them of their responsibility to keep their pet under control when out and about."