It's the fourth dog attack in Calgary since Saturday, with three suspected to involve pit bulls.
"That specific breed has caused a lot of damage in the last five days," said animal services director Ryan Jestin.
"Quite clearly there's a public safety issue here," he added.
Chastity Simon, who helps abandoned pit bulls, says Mayor Naheed Nenshi's suggestion of harsher penalties for poor pet owners might help.
The girl bitten on Wednesday suffered non-life-threatening soft-tissue injuries on both her legs, EMS officials say. She was taken to Alberta Children's Hospital.
The owner and his dog, described as looking like a pit bull, fled the scene. Calgary police and the city's Animal and Bylaw Services department are investigating.
On Monday, a 10-year-old girl and 12-year-old boy were taken to hospital with minor injuries after they were bitten by a great pyrenees dog in Abbeydale. The dog was initially reported to be a golden retriever.
Five charges have been laid in that case: having a dog-at-large, two charges of a dog chasing and threatening a person and two charges of a dog biting a person.
Two small dogs were also killed in separate attacks last weekend.
There were 400 dog bites in Calgary in 2013 and 500 in 2014.