The incident was reported to have taken place in the Bury Ditches are at Lydbury North between Clun and Bishop's Castle. It is among a number to have been reported to police in the last few weeks.
A Bishop's Castle and Rural safer neighbourhood team newsletter covering the period March 16 to April 15 said: "A dog off of a lead has chased and killed a ewe.
"The dog owner paid for damages at request of the victim."
There have also been reports of a dog on the loose attacking a ewe and lamb in Colebatch and a dog being dangerously out of control in Shelve Wood. Police said "words of advice given to dog owner at request of victim."
A spokesperson for the safer neighbourhood team said: "We are now well into the lambing season where historically it has coincided with increased reports of livestock being worried or attacked by dogs.
"Under the Dogs (Protection of Livestock) Act 1953 it is an offence to allow a dog to worry sheep, worrying includes attacking or chasing sheep.
"Dog Owners, either living locally or simply visiting the countryside for a walk, have a responsibility to keep their dogs under control at all times."
Officers say it is vital that dogs are kept on a lead around livestock, even if they can usually be trusted to come to call.
"If living in or near a farming area, please make sure that the dog is secure and cannot escape from the property," they add.
Bishop's Castle councillor Ruth Houghton has circulated the advice to her constituents, saying that there have been "worrying incidents of livestock worrying."
There have also been thefts of Land Rovers and the advice includes how to keep the vehicles secure.