The woman had been walking her dog in the Tintwistle area of Glossop during the evening of Friday, January 7.
A Derbyshire police spokesperson said: “She was at the junction of Conduit Street and West Street between 7.40pm and 7.50pm when the woman was approached by a man who demanded she gave him her dog.
“It is believed the man has then tried to take the lead of the dog, and during the process the woman suffered a cut to her hand and hip.
“He was not successful in taking the dog, and the woman’s injury is not thought to be serious.
“The man is described as around 5ft 5in tall, and of slim to medium build. He had been wearing dark clothing with a hood up and a face covering. It is thought he spoke with a local accent and had a deep voice.
“We would like to hear from anyone who may have been in the area around the time of the incident and may have noticed anything suspicious.”
Officers are also appealing for anyone with any CCTV or dash cam footage from the area at that time to contact them.
Inspector Dave Parker said: “The victim was understandably left shaken following this distressing incident, and we would urge anyone who may have noticed a man matching this description in the area around that time to get in touch.”
Call police on 101.