A woman and her pet dog have suffered painful injuries after being hit by an e-scooter in Melbourne last month.

Johanna Hersey and her beloved puppy Bella were walking through Flagstaff Gardens when a person travelling on an e-scooter hit into her.

"Suddenly an e-scooter came at full speed and went between my dog and myself," she said.

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"It basically threw me on the floor and threw Bella in the air."

Hersey fell on her face and was badly bruised from the incident and Bella, the toy poodle broke her bone in her back paw.

"It was quite traumatic for me and the dog," she said.

Three weeks on from the incident, the pair have recovered and Hersey is now calling for greater action to protect pedestrians in the CBD.

But the problem still persists, despite e-scooters being banned from footpaths.

"That bad behaviour of e-scooter's on the footpath is getting more and more common," Hersey said.

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Victoria Walks chief executive Ben Rossiter said e-scooters had the potential to be dangerous if ridden irresponsibly.

"We're seeing a lot of e-scooters being illegally ridden and the authorities have to do a lot more," he said.

It was a privately owned e-scooter that hit into Hersey and Bella.

It is illegal to ride a privately owned e-scooter on roads, footpaths or other public places.

The collision has cost Hersey, not only causing physical pain but financial, costing $1000 to fix Bella's broken paw.

The e-scooter rider stopped in the immediate aftermath of the accident and he even offered to pay the vet bills.

However, he has now gone quiet, and is ignoring all calls.