The attack sparked a hunt for the animal, involving armed officers and a police helicopter, in the city.
But the force has confirmed the dog, believed to be an American pit bull, was caught in the early hours of this morning.
Police said the attack is believed to have taken place close to an old quarry at the rear of Outer Circle Road, but an exact scene has not been identified.
The force had warned locals to steer clear of the danger zone during the search, with a spokeswoman saying: "We would ask that members of the public stay away from the area for their own safety at this time."
However, police later confirmed the dog had been caught at around 1.30am.
A Lincolnshire Police spokesperson said of the victim: "The injuries consist of a serious injury to her scalp, injuries to her face and to her arm. She remains on a ward at Lincoln County Hospital and is likely to undergo surgery later today."
The force said the dog is thought to be owned by a man known to the victim.
"This man has been arrested on suspicion of offences under the Dangerous Dogs Act and also for affray," the spokesman added.
The second offence arose from an alleged incident when police tried to seize the dog suspected of the attack from a Lincoln address. It was eventually seized and is now in police kennels, the force said.
Lincolnshire Police said it would need to carry out forensic tests to establish the exact breed of the dog, which is a white "American pit bull terrier-type of animal".
Certain types of American pit bull terrier are banned in Britain under the Dangerous Dogs Act.
Miss McCord recently posted on her Facebook page: "There's no such thing as a dangerous dog!! Just a dangerous owner!!'
Police are asking anyone who saw the attack, or who may have any information about the dog, to call the 101 non-emergency number and quote incident number 521.