Abdallahi, 70, immediately left the residence, travelling 250km to his home in Lemden, apparently preferring to arrive in the capital according to his own agenda.
One of his officials said that he had been driven to Nouakchott "against his will".
The former president had been under house arrest in the southern village since August 6 when the military took power in a coup.
He had turned down an invitation to attend talks organised by the military rulers next week, saying it would legitimise the coup, France's Le Monde newspaper reported on Saturday.
Observers said his release may be designed to encourage him to enter into talks.
Amid mounting international pressure, the rulers had recently announced that the former president would be freed unconditionally before the end of December.
Abdallahi said her father had never been informed directly about the plan.
The deposed president was elected for five years in 2007, becoming the country's first democratically elected leader.
He served for 15 months before the coup by a group of generals led by Mohamed Ould Abdel Aziz.
Abdallahi had attempted to remove Abdel Aziz, a presidential guard chief, after becoming president.
The US and France suspended aid to the west African nation after the coup and the EU has threatened sanctions against it.
Mauritania has had numerous coups since independence from France in 1960.