Police are hunting two men over the incident in Ramsay Road, Kirkcaldy, at around 7.45am on Friday.
A 47-year-old woman was walking her three dogs in the road when she became aware of a man running behind her.
Shortly after he passed her, another man approached the victim and tried to take her handbag.
During the struggle one of the woman’s dogs bit the man’s leg and he ran off towards Pratt Street.
The first man was described as being in his 20s, around 5ft 8in and was wearing dark joggers and a light coloured hoodie with his hood up.
The second man, who attempted to steal the bag, was also in his 20s, around 5ft 5in, with dark hair and a “gaunt” face.
He was wearing a dark coloured cap with blue denim jeans and a dark coloured tracksuit top.
Detective Sergeant Craig Fraser said: “We’re appealing to anyone who might recognise these men, or may have witnessed this incident.
“The suspect shouted when he was bitten by the dog, and it’s possible he may have struggled to walk properly afterwards.
“If anyone has any information, please contact us.”