He had surgery in the capital, Nouakchott, and will receive further medical treatment in France.
Before leaving, Mr Abdelaziz, 55, appeared on television from his hospital bed to say he was OK.
A military patrol is said to have mistakenly opened fire on the presidential convoy late on Saturday.
“I want to reassure the citizens of Mauritania that the operation I underwent yesterday [Saturday] evening was a success thanks to the efficiency of the medical team that carried it out,” he said.
Earlier, Communications Minister Hamdi Ould Mahjoub said Mr Abdelaziz was injured in the arm and that his life was not in danger.
A medical source told AFP news agency that he had had a bullet removed.
It was not clear what treatment he was going to receive in Paris, says BBC Arabic’s Mohammad Taha in Nouakchott.
The country is being run by the prime minister in the president’s absence.
He is expected to open an inquiry into the shooting and two army officers have reportedly been detained on suspicion of involvement.
Initially, Mauritanian radio reported Mr Abdelaziz had escaped an assassination attempt.
Many Nouakchott inhabitants tend to believe the “shot by mistake” claims as they are used to seeing the president walk in the city, play sport and drive his car without guards, our correspondent says.
Some local reports say the president was targeted by a militant group while travelling from Tweila, north of the capital, where he spends most weekends, our correspondent says.
He was travelling overnight to the capital as the week starts in Mauritania on Sunday.
President Abdelaziz came to power in a military coup in 2008 in the West African nation. He won presidential elections a year later held under an agreement with coup opponents.
The BBC’s Mohammed Taha says coups and coup attempts are almost a normal part of life in Mauritania, with three in the last ten years. The military has been involved in nearly every government since the country became independent from France in 1960.
The current president is seen by the West as a bulwark against Islamists in the region, particularly in neighbouring Mali.
Mauritania launched a joint military operation with Mali last year against the bases of Islamist militants in Mali before a rebellion in that country this year split it in two and hardline Islamists occupied the the country’s vast northern region.