Travis Nielsen's daughter, Bree, suffered some puncture wounds in the sudden attack, but is otherwise doing fine.
"She was crying but she's OK," said his wife, Andrea Nielsen. "She's got some small puncture wounds just above her right ear, one on her back and then a couple on her chest."
The cougar pounced while the three of them were sitting in their backyard in Tahsis on the west side of Vancouver Island.
"(Bree) was sitting with a six-week-old puppy and we were just kind of looking at the ocean and enjoying the day and then all of a sudden from behind the shed, my daughter was attacked."
Nielsen told The Canadian Press it wasn't immediately clear what kind of animal had the toddler.
"At first, we thought it was a large dog. But then we realized — after my husband pulled my daughter out of the way and punched it in the face — that it was actually a cougar."
The cat dropped the girl and Travis Nielsen yelled at the cougar to "get out of here."
"He was still out there scaring the cougar into the forest even after the fact, once we were all safe in the house," said his wife.
Conservation officers eventually put the animal down and scoured the area for any additional big cats.
"They sent in a team and they had bloodhounds with transmitters on their necks," said Andrea Nielsen. "They were going through the forest and they set up traps."
She said it had been "an intense day." Asked how long it might take for her family to stop shaking, Nielsen replied: "Never."
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