According to results of a quick count by a private polling company, the proposed reforms were backed by 56.8 per cent of voters and opposed by 43.2 per cent, with more than 90 per cent of precincts reporting.
Elections: Presidents would be allowed two consecutives five-year terms
Indigenous rights: Recognises self-determination of 36 'nations' and sets aside seats in Congress
State control for all gas, oil and mineral reserves
Local autonomy: Authorises state assemblies that control local issues and self-rule for indigenous groups on traditional lands
Justice: High court judges to be elected rather than appointed
Equality: Prohibits discrimination on sexual orientation and guarantees freedom of religion
If the results are confirmed the new constitution would give indigenous Bolivians a share of profits from natural resources and greater access to government.
But the proposed reforms have put the country's indigenous people at odds with Bolivia’s elite, who are traditionally of European descent.
"We await your participation in this democratic celebration," Morales said on local radio, ahead of Sunday's vote.
"This is the first time a constitution will be voted on by the Bolivian people."
Bolivia's Aymara, Quechua, Guarani and other indigenous groups only won the right to vote in 1952.
The proposals include a larger state role in the economy, grants of self-rule to 36 distinct indigenous "nations" and a December general election, in which Morales could run for another five-year term.
Voters also decided on whether future land ownership should be capped at 5,000 or 10,000 hectares. The state could seize land that does not perform a "social function" or was fraudulently obtained.
"This new constitution of the Bolivian state wants to give everybody the same opportunities, the same rights and the same duties. And there shouldn't be exclusion anymore," Morales said in the capital La Paz on Saturday.
|Nearly four million Bolivians were registered to vote in the referendum [AFP]
Morales strong support is likely to see the referendum passed. He won 67 per cent of the vote in a recall referendum in August 2008.
"Evo Morales will win, because he is a good president and he is helping children and old people. So we will vote 'yes'," Norita Manami, a Morales supporter, said.
But despite strong support for Morales, the vote could prove divisive with the country split along geographic, racial and class lines.
The opposition, led by state governors in the more prosperous east, has objected to the proposed changes and opponents of Morales still hold a majority in the senate.
Al Jazeera's Latin America Editor, Lucia Newman, said that is likely to prove problematic because even if the constitution is formally approved, it will require hundreds of new laws to be passed by congress to support the articles it contains.
Many critics have accused Morales of harming the economy through the nationalisation of a number of businesses.
"This is a false referendum, it does not have the participation nor the support of half of the Bolivian people. We people from the east [the lowlands of Bolivia] don't expect anything good from it," Percy Ruiz, an opponent of Morales, said.
However, the opposition allowed the referendum to go ahead after Morales agreed to stand for only one additional term and grant greater autonomy to the regions.
Nearly four million Bolivians were registered to vote in the referendum monitored by international observers.