The army said troops found Salomi Pugo in the remote Pulka region of Borno state near the Cameroon border, without giving further details.
The abduction of more than 200 Chibok schoolgirls in 2014 by Boko Haram brought global attention to the Islamist insurgency sweeping through northeast Nigeria.
"Troops of Operation Lafiya Dole deployed in Pulka today rescued one of the Chibok girls abducted by Boko Haram terrorists earlier in 2014," Colonel Onyema Nwachukwu said in a statement.
News of the rescue comes after weeks of relentless attacks by Boko Haram in the northeast, including the abduction of 30 loggers and a suicide bombing that claimed 14 lives at a mosque in Gamboru in Borno state earlier this week.
At least 30 soldiers are also missing following a Christmas Day attack on a military base in neighbouring Yobe state in which five troops were killed, according to military and militia sources.
Since then, others have been freed in hostage deals struck between Boko Haram and the Nigerian government, but many are still in captivity and some are feared dead.
Since 2009, the Boko Haram insurgency has spread from Nigeria into neighbouring Niger, Chad and Cameroon and affiliated itself with Islamic State jihadists.
Despite the ongoing attacks, Nigerian President Muhammadu Buhari said in his New Year address that Boko Haram was "beaten".
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