However, a spokesman for the AU said the country will remain in the group but will not be able to participate in meetings or votes until its "constitutional order" is restored.
Mauritania is no stranger to coups since it gained independence from France in 1960.
Abdallahi's election was hailed as a model of democracy for Africa, after a three-year transition after a bloodless coup in August 2005.
President held captive
For his part, General Mohamed Ould Abdel Aziz, Mauritania's coup leader, has vowed to keep Abdallahi captive until further notice for security reasons, according to an interview published on Saturday.
"We will not release the ousted president at the moment for security reasons," he told Asharq al-Awsat, the Arabic-language daily, in a telephone interview.
"We are trying now to establish calm and de-escalate the situation."
Abdallahi was overthrown after he tried to sack Aziz and other senior army officers.
On Thursday, security sources said he was being held at the headquarters of the presidential guard, and on Friday he was reported to have been moved to a villa.
"The former president is fine and in good health. He has no problems. There is a new authority - the state's supreme council, which will look into the case of the president dossier after putting the country's internal affairs in order. This will take some time," Aziz said.
Although the new junta promised on Thursday to hold presidential elections after the "shortest possible period," Aziz failed to commit to a date.
"It is difficult to give a set date for the presidential elections at the moment because we are addressing the priorities of the country and the needs of the people which were long ignored by the former president."