A young man was killed during the protests after apparently being hit by an exploding tear-gas canister, a hospital source said.
A local government source confirmed the death but said the circumstances and cause were yet to be clarified, according to AFP news agency.
The violence began after four people dressed in turbans were reported to have driven to a mosque in the north of Nouakchott and taken copies of the Quran to destroy.
Local media reported that on Sunday night four people entered a mosque in the Teyaret neighbourhood and tore up Qurans and threw them on the floor. It was not immediately clear who was behind that attack or what their motive was.
One of them “took four copies of the Quran which he shredded before throwing them in the toilet,” the local imam said.
Police fended off a large crowd bound for the presidential palace shortly after midnight,according to Reuters news agency.
Communications Minister Sidi Mohamed Ould Maham called for protesters to return home at a news conference on Monday.
The country operates Islamic law courts but the death penalty has not been applied for blasphemy since the 1980s.
A young Muslim is facing a possible death sentence after being convicted in January of apostasy and jailed for having written an article criticising the Prophet Muhammad.
In February a man was arrested and sent for psychiatric evaluation after urinating on a Quran in northern Mauritania.
President Mohamed Ould Abdel Aziz, who has been an ally of the west in its battle against al-Qaeda in the poor and unstable Sahel region, is up for re-election in June.