Police shot the animal dead after it bit the little girl in the Jenkins Dale area of Chatham, Kent, on Tuesday evening.
The child was taken to a London hospital while critically ill but her condition has since improved.
A Kent Police spokesman said: "The child continues to be treated for very serious injuries, but these are no longer described as life-threatening."
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A man and a teenager, both from Chatham, were arrested on Tuesday under the Dangerous Dogs Act and remain in police custody.
A third person, a woman also from Chatham, was detained on Wednesday.
A neighbour said she heard a gunshot and saw the child being carried to an ambulance.
The attack came two days after armed police shot dead two pitbull-type dogs that attacked a man and woman in the street in Bolton, Greater Manchester.
Officers were called to Queen's Park in Chorley New Road on Sunday after reports that five dogs were dangerously out of control.
Daniel Hennessy, 39, has been charged with allowing dogs to be dangerously out of control.
As inquiries continued in Chatham, Kent Police said they were trying to establish the breed of the dog and appealed to members of the public with footage of the incident to contact them and not to share it on social media.
One man wrote on Facebook: "Personally knowing the family and the child involved and seeing the aftermath of such an event has shocked me!
"Hoping the little girl ,which I will not name, is ok and is in the best possible care. I'm with the sister now who is shocked and shaken."
Jaspreet Uppal, who lives nearby, told the Press Association: "First I heard a gunshot, there was a dog on the floor. A few officers carried out a child from the back area of the flats.
"There is a little park there. I could not see the child, they were covered. I think they were quite small."
Local MP Tracey Crouch said: "Horrible news from Chatham this evening. My thoughts and prayers are with the child and their family tonight."