Police said the attack involving a 17-year-old pit bull-rottweiller cross happened around 1 a.m. PT. in the family home.
The baby is in hospital in stable condition.
The family agreed to have the dog put down, said Saanich police Const. Nawid Akbar.
Akbar said the investigation is ongoing, but charges of criminal negligence are being contemplated.
He said it's important to remember animals can be unpredictable
"When you have small children, especially children who can't care for themselves, and when they're as young as a 16-day-old baby, it's a reminder that when you have pets in the home, it's very important to be aware of your pets as well as your children because at the end of the day, pets are animals and you don't know what they're going to do.
Akbar said the injuries appear to be superficial and not likely to cause long term damage, but it's still too early to be certain.