The polls in the impoverished Islamic republic, which straddles Arab and black West Africa, are the first since a military junta seized power in a bloodless putsch last August. It will lay the foundation for a presidential election next March.
If approved, the changes will make Mauritania one of few Arab nations to limit the number of terms a president can serve, and set it apart from sub-Saharan Africa where several leaders have amended rules to keep themselves in power.
"This is a day of change for Mauritania. I am proud and optimistic," said Alpha Youssouf Diagana, a retired soldier queuing to vote in the sand-blanketed capital, Nouakchott, on Sunday.
Power has never changed hands through the ballot box in Mauritania, Africa's newest oil producer and a country of just three million people on the western edge of the Sahara.
Last August's coup was met with widespread jubilation after repeated failed bids to oust former President Maaouya Ould Sid'Ahmed Taya, whose authoritarian rule stretched through two decades.
"It is a historic day for Mauritania. It is truly the rebirth of politics in this country," Colonel Ely Ould Mohamed Vall, head of the ruling military council, said after casting his vote in the Ksar district of Nouakchott.
Speaking to Aljazeera from Nouakchott, Sheikh Sidi Ould Hannana, leader of the Mauritanian al-Sawab (reason) Party, said voting has been impressive.
"We encouraged our supporters to head for polling centres to vote "yes" to herald a new stage in the history of Mauritania", he added.
He said the reforms will secure freedom and democracy that Mauritanians have longed for.
Men in traditional white and blue robes and women clad in bright fabrics lined up in front of schools and government buildings serving as polling stations.
Electoral officials said that by halfway through the day, the turnout was above 30% across the country as a whole. Some polling stations in Nouakchott reported a turnout of 50%.
Some polling stations reported
a voter turnout of 50%
Initial results are expected on Monday.
The proposed changes to the constitution would prevent a president from standing for office more than twice and limit the term to five years instead of six.
They would also make it harder for future leaders to change the rules once in office.
"We want change, no more presidents who stay for 10 or 20 years," said unemployed Omar Sidi Bathily Ba, 26, emerging from a dimly lit polling booth, his index finger marked with indelible ink used to stop people voting twice.
Mauritania's main parties, unions and religious groups have lobbied in favour of the amendments but officials acknowledge the biggest challenge is persuading a public used to polls marked by intimidation and fraud to come out and vote.
"Not all young people will vote. They're used to being paid to do so," said Mar Ba, 25, a singer with the popular local rap group Diam Min Teky. "But every citizen should do so and participate in the development of our country."
Some Mauritanians, particularly those of black African descent, say the changes do not go far enough, failing to address deep-seated inequality in a country where power has long been concentrated in the hands of an Arab elite.
They say the constitution should also be changed to include laws formally abolishing slavery and making French one of the country's official languages alongside Arabic, not widely spoken among the black African community.