The one-year-old Spaniel died after being shot twice during the incident on a farm in Ballingry, Fife.
Under Scots law, farmers are allowed to shoot dogs on their land if they are concerned the animals may attack or leave their livestock distressed.
The dog owner's sister, Lorraine Daly Armstrong, took to social media to warn others to keep their pets on leads.
She wrote: “Just a warning to everyone walking their dog, this wee precious spaniel lost his life because he entered the field where sheep were.
“He didn’t attack any, he ran back to get his owner and was shot twice at and once straight in the head.
“Please don't walk your pets near fields, not off a leash.”
Sergeant John Nicol, of Cowdenbeath Police Station, said: “Around 11.55am on Tuesday, 23 March, 2021, police were made aware that a dog was shot and killed on a farm in the Ballingry area following an incident of sheep worrying.
“Officers attended to carry out enquiries and no further action was required.
“Instances of sheep worrying cause a great amount of emotional distress and often substantial financial loss to farmers.
“And in this tragic case, the dog owners have also suffered personal heartache as a result of the attack.
“The lambing season has started, so anyone exercising dogs should make sure they keep their pets on a lead and under close control when walking near livestock.”
It comes as new legislation passed that could see dog owners fined up to £40,000 or jailed for a maximum of a year for livestock worrying.
Yesterday, Holyrood unanimously backed a member's Bill brought forward by SNP MSP Emma Harper, who said the change would help make a "real difference to farmers".
She said she wanted to "help to educate everyone about the importance of keeping dogs under control around livestock".
Ms Harper, a dog owner, added: "It's lambing season now, the fields are full of pregnant ewes and new lambs, it is very distressing to see the photos of carnage of dead sheep and lambs from attacks by out of control dogs."