Before his departure, Aziz delivered a speech via radio assuring the country he was in good health and there was nothing to "worry about," China's Xinhua News Agency reported.
Government spokesman Hamdi Ould Mahjoub described Saturday's shooting to the state-run AMI news agency as "friendly fire" from a military unit.
The shooting happened as Aziz was returning to the capital, Nouakchott, from his farm, CNN reported.
While the government said the shooting was an accident, witnesses told an independent Mauritania news agency it appeared to be an assassination attempt, as the shooters fled after opening fire, while soldiers remained in their station.
Various Western intelligence agencies have acknowledged the presence of an al-Qaida sect in the coastal West African country.