Police said the animal's owner had been arrested and the dog, believed to be an American pit bull, was now in kennels.
Armed police and a helicopter were deployed to search for the dog after the attack on Sunday.
Insp Michelle McIlroy, of Lincolnshire Police, said the victim, 22, had suffered "life-changing" injuries.
She had also suffered "deep facial gouges on her cheeks" and injuries to her hand, said Insp McIlroy.
In the UK it is illegal to own certain types of dog.
Pit bull terriers, Japanese Tosas, Dogo Argentinos and Fila Brasileiros are banned.
But whether a dog is classed as illegal under the Dangerous Dogs Act 1991 depends on what it looks like, rather than its breed or name.
The police and council dog wardens have the power to seize dogs even in the absence of a complaint.
They will then judge its characteristics and decide whether it should be released or an application made to the courts for it to be destroyed.
The maximum penalty for owning a banned dog is a Â£5,000 fine and/or six months in prison.
Source: Gov.uk
Residents in part of Lincoln were warned to stay in their homes during the night-time search for the animal.
Police searched an area near an old quarry off Outer Circle Road on the outskirts of the city on Sunday evening.
During the search, the area where the dog was thought to be was "contained" by police.
The woman was taken for treatment to Lincoln County Hospital.
Insp McIlroy said: "She has suffered quite devastating injuries. They are not described as life-threatening, but certainly life-changing.
"It is quite unusual for an adult to be attacked by a dog in this way. We hear about small children being attacked but it is unusual for an adult to be attacked."
Tests are being carried out on the dog to confirm the breed, police said.
Insp McIlroy said magistrates would be likely to approve a destruction order for the dog.
A 33-year-old man has been arrested on suspicion of having a dangerous dog out of control in a public place.
He will also be questioned on suspicion of affray after an incident involving police officers who were attempting to seize the dog.
Injuries described as "devastating" to a woman attacked by a dog in Lincoln, include having the skin on her head "ripped back exposing her skull".