Vancouver Aquarium said it had been contacted by the girl's family after staff had raised concerns about "seal finger", which can lead to amputations.
The girl suffered a 10cm (4in) wound when the animal grabbed her with its jaws, her father told CBC News.
He rejected claims that she had been trying to feed the marine mammal.
The video of her being pulled by the dress from the dockside in Richmond, British Columbia, and then rescued by her grandfather, has been widely shared on social media, prompting some users to suggest the family had  been trying to feed sea lions.
"There was somebody beside them that was trying to feed them," said the father, who gave only his surname, Lau, in order to prevent the identification of the girl.
But he admitted his daughter had got too near when she moved forwards to have a closer look.
"That's a lesson she took and she has taken that lesson in a hard way," he said.
Aquarium spokesman Deana Lancaster told ABC news the family had got in touch after staff gave interviews about the risks of "seal finger" infection.
Bacteria living in the mouths of seals and sea lions can cause the painful and potentially serious condition, with symptoms including cellulitis and debilitating joint inflammation.
It is mainly known historically for affecting sealers' hands, although it can travel to any part of the body.
Ms Lancaster said the girl was now going to get the right treatment.
Mr Lau confirmed the family had been in touch with the aquarium and praised the girl's grandfather's quick response.
"If he had a one- or two-second doubt about that, my girl could have been gone by then. That reaction makes him a hero," he said.
He said the family had been "disturbed" by the video going viral, but were mainly just relieved the girl was safe.
"Only thing I care is: God, she is safe," said Mr Lau.
"I could have gone organising a funeral by now rather than doing an interview."

The 22-year-old is Vale's top scorer so far this season, having scored eight times in 12 league games.
Jones' deal is set to expire in January but Vale are keen to keep him, and would prefer to sign him outright.
"I think the way forward is to acquire him as a contracted player in January," Smurthwaite told BBC Radio Stoke.
"I'm in the process of building a football club. He's embraced the club very well. He's a great lad and he'd be a great addition to our squad.
"I've spoken to Birmingham and put forward a proposal."
Smurthwaite says one of the club's brightest young talents may end up leaving.
Defender Nathan Smith, 20, won the EFL's Young Player of the Month for August after making his league debut at the start of the season and was rewarded with a new three-year contract extension.
"There's some interest from the Premier League," Smurthwaite said.
"I'll be honest, if the right offer is made and Nathan wants to go, he'll be leaving us in January.
"This lad isn't motivated by money, he's motivated by the craft and if it's not right for him, he won't go.
"When the right opportunity comes for him, Port Vale will be recompensed but he will control that decision, not us."
A girl dragged off a dock in Canada by a sea lion is being treated with antibiotics because of the risk of a dangerous infection.
[NEXT_CONCEPT]
League One Port Vale are trying to sign on-loan striker Alex Jones permanently from Birmingham City, says chairman Norman Smurthwaite.