The poll in the Arab West African country asked voters on Sunday to approve constitutional changes that would prevent a president from serving more than two terms, each of them limited to five years.
The interior ministry said early on Monday that 80 to 90% of the voters backed the proposals, estimating the turnout at between 65 and 73%.
It said that the figures were provisional and had yet to be confirmed.
Official results are expected to be announced by the government on Monday.
If confirmed, the result would make Mauritania one of a few Arab nations to limit presidential terms and set it apart from sub-Saharan Africa, where several leaders have amended constitutional rules to keep themselves in power.
Sunday's vote was the first step in the transition process due to culminate in presidential polls next March.
International observers said the referendum, in which just under a million people, roughly a third of the population, were registered to vote, appeared to have gone smoothly.
Previous polls in the former French colony, where power has never changed hands through the ballot box, have been marred by widespread irregularities, including multiple voting and intimidation by the army.