The first attack happened at Upper Gate House in Dinedor at about 9am on 30 May.
Then at around 6am on 1 June, it was reported that two dogs went onto the same field and struck again. It is believed one of the dogs was the same dog as the first attack.
Some time between 10pm on 31 May and 6am on 1 June, a sheep farmer at Lower Huntless Farm in Twyford, which is around one mile away from the other two incidents, reported that his flock had also been attacked by a dog.
A vet confirmed the injuries to the sheep were caused by a dog.
Sergeant Mark Jones from West Mercia Police said: "These are very concerning incidents which are causing a lot of anguish and financial damage for the victims and we are working closely with the farming community to help them maximise security for their flocks.
“We can only roughly estimate how many sheep have been killed based on what farmers have told us – we are aware of separate incidents of five, 11 and 12 sheep being killed at different farms so it seems to be as many as 28."