Officials say it was an accident, but there are suspicions it may have been an assassination attempt by al-Qaida.
Mohammed Ould Abdel Aziz himself led two coups in the northwestern African state, the last one in 2008 in which he took power.
He's long been a leading opponent of the jihadist forces operating in the region.
The suspicions of an al-Qaida hit hinge on Abdel Aziz's efforts to crush the jihadist network that has swelled across the region and in particular his support for military intervention to crush al-Qaida's North African affiliate and its Islamist allies who seized control of two thirds of neighboring Mali in the spring.
If jihadists were involved in Saturday's shooting, that would likely intensify pressure on the United Nations to approve military intervention against the jihadists, which could ignite violence across North Africa.
The shooting of Abdel Aziz -- accidental or not -- took place at a checkpoint 25 miles northeast of the capital Nouakchott after nightfall as he drove returned from a regular weekend break at his ranch, his country retreat.
Officials say a military patrol failed to recognize the presidential convoy, in which Abdel Aziz was driving his own car, and opened fire.
Reports vary, but most confirm he was hit in the arm or abdomen, or both. Communications Minister Hamdi Ould Mahjoub said Abdel Aziz was "lightly wounded and his life is not threatened."
He was hospitalized in the capital. "Thank God, I'm doing well," he said in a televised statement from his hospital bed.
But despite reports he was doing well, he was flown to France, the former colonial power, Sunday for unspecified treatment at a military hospital.
There was no official explanation for that, raising questions about his condition and indeed the shooting itself.
Local commentators have questioned official accounts, asking why Abdel Aziz was traveling without bodyguards, why the checkpoint did not his convoy was approaching and if his injuries were light why he was moved to France.
If indeed the shooting was not accidental, it's generally believed Abdel Aziz, widely seen as a despot with no lack of enemies, was attacked by gunmen linked to AQIM.
It has issued several death threats against him for his hard-line crackdown on Islamist militants.
In July, one of al-Qaida's top ideologues, the veteran Abu Hafs al-Mauritani, returned to his homeland from Iran, where he had lived since late 2001.
It's not clear whether he's actively engaged in jihadist operations, and there's no evidence he was involved in the shooting of Abdel Aziz.
But with AQIM running northern Mali, his presence in Mauritania should be a cause for concern.
Mauritanian forces, which have been aided in the past by French Special Forces, mounted repeated attacks on AQIM bases in Mali before a March rebellion split the country in two.
Heavily armed Islamists, spearheaded by AQIM, seized control of the northern region and declared an Islamist state. Regional and Western powers fear it will provide a launchpad for jihadist attacks across the Sahel and even into Europe.
Abdel Aziz's government would be a key component of any regional intervention against al-Qaida and its allies in Mali.
The 15-nation Economic Community of West African States has proposed sending in a 3,000-strong force, provided the U.N. Security Council gives its approval.
Earlier this month, U.S. officials disclosed the White House had held secret meetings to examine the Islamist threat in Mali and to consider unilateral military strikes.
France has had a score of citizens kidnapped by AQIM and has commando units on the ground in North Africa. It favors military action to eliminate the jihadist threat. Several Western powers support intervention.
U.S. Special Forces have been reported moving into position for a possible strike, particularly following the Sept. 11 killing of the U.S. ambassador in Libya, Christopher Stevens, and other Americans in Benghazi, supposedly by jihadist operatives.
The Americans are reported to be considering extending missile strikes by unmanned aerial vehicles, widely used against jihadists in Yemen and Somalia, to North Africa.
AQIM and its allies in northern Mali were reported Oct. 8 to be bracing for a major offensive against them and to be building up their defenses.