The president was wounded in the stomach and has already been operated on in Nouakchott, a source told Reuters news agency, while another told AFP that he is to be transferred to Paris.
The government denied an earlier report that Aziz was targeted in the attack on Saturday.
"This was an accidental shooting on the presidential convoy as it returned to Nouakchott. The army unit did not recognize the presidential convoy," Communications Minister Hamdi Ould Mahjoub said on national television.
"The Mauritanian people can be reassured, the president is fine... He was slightly wounded, and he got out of the vehicle unassisted upon arrival at the hospital, where he walked in without difficulty."
Aziz was involved in two coups d’état, in 2005 and 2008, and took the leadership of the country. He was elected president in 2009 in an election that opponents say was not free and fair.