The video, recorded on Richmond Road in Sheffield earlier this month, shows the woman screaming as the Staffordshire bull terrier runs into the shot and starts to attack. The mother had been with her own dog and her one year old daughter, who was on a trike.
A man is then seen rushing in to try to pull the attacking dog off.
The video has been released by South Yorkshire Police to highlight what they have described as an on-going problem of owners not taking responsibility for their dogs' actions - and the severity of what can happen.
The woman was walking her dog along Richmond Road on September 2 and her one-year-old daughter was alongside them on a trike, when an unknown dog approached them.
The dog, a Staffordshire bull terrier, had escaped its owner and began attacking the victim’s dog, which required treatment from a vet. The woman and her daughter both suffered superficial injuries.
Police say the footage released shows how incidents involving loose dogs and those not under control can quickly escalate and lead to serious injury.
South Yorkshire Police dog legislation officer PC Paul Jameson is urging dog owners to take action, at a time when dangerous dogs have been in the news following a number of incidents involving serious injuries and even death. Another recent incident in Sheffield saw a dog attack a man on Handsworth Road, with armed police sent to the scene.
He said: "Your dog is your responsibility. If it attacks someone or causes fear in our communities, you are the one held responsible, you are the one facing prosecution, but your dog could also face being euthanised.
"If you know your dog can escape your garden, fix it. Build higher fences, put a lock on the gate, put up signage for people to be aware, and not enter.
"Keep your dog on a lead, and if you know your dog doesn’t like other dogs, walk it in quieter areas and not during busy times.
"They’re animals, even the most relaxed animals in certain situations can be subjected to stress, which may cause a response born from fear. It’s an animal’s instinct and it’s our role to understand those situations, spot the signs your dog is giving you and remove them, or the stressor.
"Dogs think like dogs and it’s dangerous to apply human thinking to a dog’s behaviour.
"The same goes within your own home; teach your children from a young age to respect dogs, don’t let them climb or jump on them, ensure your dog has somewhere quiet to go that is their space, away from family life.
"Sometimes simple common-sense, low-cost changes can make the difference."
The dog in the footage was seized by officers, but later returned to the owner with conditions and guidance to follow.
The owner of the dog is being processed through 'restorative justice' for the harm caused to the victims.