The incident took place after the girl and her father went out for a walk near their home in the village of Ås. They spotted the beaver at the side of the road and the girl decided it would be fun to pet the animal, newspaper Östersunds-Posten reports.
But the beaver had other ideas and quickly lunged at the girl. The attack was filmed by the girl's father, Marcus Handler, who was standing ten metres away.
"What I was seeing through the camera seemed unreal. I just screamed 'no, no' and rushed towards Matilda. Then the beaver started attacking me instead but I managed to jump out of the way and grab hold of Matilda," he told the Östersunds-Posten newspaper.
With his daughter bleeding profusely from one of her wrists and one of her thighs, Handler flagged down a passing car and had the girl taken to a nearby clinic for treatment.
A week has now passed since Matilda's unexpectedly violent brush with the animal kingdom and the girl is eager to speak about her trauma.
"It jumped on me and started biting. I was bleeding a lot. It was silly," she said.
Asked what she would do if she ever bumped into the beaver again, Matilda said she would "sword it with a sword".
Maano Aunaduu, a local zoologist, believes the animal felt threatened by the four-year-old.
"It did exactly what a dog would have done in a tight situation," he said, adding that it was never advisable to pet a wild animal.
He did however concede that Matilda's experience was rare.
"It's the first time I've ever heard of anyone being bitten by a beaver," he said.