The girl, found along with her baby son, was one of the more than 200 schoolgirls taken by the Islamist group from their hostels in the remote town of Chibok in April 2014.
Dozens of the girls escaped in the hours after the kidnapping but more than 200 are still unaccounted for.
The mass abduction drew global anger and attracted unprecedented attention to the seven-year Boko Haram insurgency.
News of the latest rescue came barely a month after 21 other Chibok girls were released by Boko Haram.
Army spokesman Sani Usman told AFP that "Nigerian army troops rescued another Chibok schoolgirl at Pulka," in Borno state near the Mandara mountains separating Nigeria from Cameroon.
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Usman later said in an official statement the girl was rescued "at about 6:00am while (the army was) screening some escapees from Boko Haram terrorists hideout in Sambisa forest."
He identified her as Maryam Ali Maiyanga, adding that she was carrying a 10-month-old son.
"She has been taken to the unit's (army's) medical facility for proper medical check up," he said.
The Bring Back Our Girls (BBOG) lobby group confirmed the release.
"We are happy with the news... We have confirmed the name of the freed girl to be among those on our database," BBOG campaigner Aisha Yesufu told AFP.
"Our hope is that the government will work towards an early release of the remaining girls so that we can bring this sad episode to a close," she added.
BBOG later said in a statement on Saturday that "preliminary investigations on our part, show that Maryam Ali (Number 198 on our list), a school prefect, is from Askira Uba and was abducted along with her twin, Halima Ali (Number 197), who is yet to return."
The group, which has been at the vanguard of local campaigns to free the girls, commended "the federal government under President Muhammadu Buhari, the military and other security formations working day and night to rout the terrorists and rescue all Nigerians in captivity."
The 21 Chibok girls released last month were freed following negotiations between the Nigerian government and Boko Haram, brokered by the International Committee of the Red Cross (ICRC) and the Swiss government.
Local residents in the town of Barki where the 21 were freed said they were exchanged with four Boko Haram prisoners, but the government denied this.
The government said at the time it had received a commitment from Boko Haram to secure the release of 83 other girls believed to be from Chibok being held by a different faction of the extremist group.
Usman said Saturday "it is imperative to state that troops have been working round the clock to clear remnants of Boko Haram terrorists wherever they might be hibernating and also rescue all persons held hostages by terrorists".
Boko Haram's insurgency in Nigeria's mainly-Muslim north has killed at least 20,000 people and made more than 2.6 million homeless since 2009.
