Already the country's longest serving leader, the 56-year-old Morales cast his ballot in the coca-growing region of Chapare where he first emerged as a political force to become Bolivia's first indigenous president in 2006.
Monitors from UNASUR, a regional political union, said polls opened "in a climate of absolute calm" in Bolivia, a major gas and mineral producer but one of South America's poorest countries.
But angry voters set fire to ballots and ballot boxes at a polling station in the city of Santa Cruz after they learned there were no election registries, a spokesperson for the regional election tribunal said.
Polling station began to close at the scheduled 4:00 pm (2000 GMT) deadline, but election authorities extended voting in some places.
Local television stations are expected to air exit polls a few hours after the voting ends, with official results to follow.
Urging supporters to turn out in record numbers, Morales -- an Aymara Indian -- exhorted them to "let us know if they love me or not" by endorsing changes in the country's constitution to allow him to run for a fourth term.
A late breaking corruption scandal involving an ex-lover of Morales appears to have hurt the campaign for a "Yes" vote, however.
Since taking office the first time in 2006, Morales has been re-elected twice, most recently in 2014 to a five-year term that ends in 2020.
Under the current constitution adopted in 2009, sitting presidents can only seek re-election once.
But Bolivia's Supreme Court ruled that Morales's first term was exempt from the rule, allowing him to run again in 2014.
The campaign formally ended on Thursday but continued furiously on social media sites like Facebook and Twitter throughout the weekend.
Voting is mandatory, and some 6.5 million Bolivians are eligible to cast ballots.
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