Among the first to vote was Muizzu, 45, who cast his ballot at the Tajuddin school in the capital Male and urged Maldivians to ensure a high turnout -- which would be expected to favour him.
"All citizens should come out and exercise their right to vote as soon as possible," Muizzu told reporters after casting his ballot in the capital Male, where he was mayor before winning a presidential election in September.
Election chief Fuad Thaufeeq said after polls closed that turnout had already reached 73 percent of the 284,663 electorate when half an hour of voting remained.
Results were expected early Monday.
The vote is seen as a crucial test for Muizzu's plan to press ahead with closer economic cooperation with China, including building thousands of apartments on controversially reclaimed land.
The Maldives, a low-lying nation of some 1,192 tiny coral islands scattered some 800 kilometres (500 miles) across the equator, is one of the countries most vulnerable to sea level rises caused by global warming.
Muizzu, a former construction minister, has promised he will beat back the waves through ambitious land reclamation and building islands higher, a policy which environmentalists argue could even exacerbate flooding risks.
The Maldives is known as a top luxury holiday destination thanks to its pristine white beaches and secluded resorts, but in recent years it has also become a geopolitical hotspot in the Indian Ocean.
Global east-west shipping lanes pass the nation's chain of 1,192 tiny coral islands, which stretch around 800 kilometres (500 miles) across the equator.
Muizzu won last September's presidential poll as a proxy for pro-China ex-president Abdulla Yameen, freed last week after a court set aside his 11-year jail term for corruption.
- Indian troops leaving -
This month, as campaigning for the parliamentary elections was in full swing, Muizzu awarded high-profile infrastructure contracts to Chinese state-owned companies.
His administration is also in the process of sending home a garrison of 89 Indian troops who operate reconnaissance aircraft gifted by New Delhi to patrol the Maldives' vast maritime borders.
The current parliament, dominated by the pro-India Maldivian Democratic Party (MDP) of Muizzu's immediate predecessor Ibrahim Mohamed Solih, has sought to stymie his efforts to realign the archipelago's diplomacy.
"Geopolitics is very much in the background as parties campaign for votes in Sunday's election," a senior aide of Muizzu told AFP, asking not to be named.
"He came to power on a promise to send back Indian troops and he is working on it. The parliament has not been cooperating with him since he came to power."
Solih was also among those voting early and expressed confidence his party would emerge victorious.
"We hope the MDP will be able to secure a good majority by the end of today's voting," he said. "We have been seeing this happening today and during the campaign."
Since Muizzu came to power, law makers have blocked three of his nominees to the cabinet and refused some of his spending proposals.
Splits in all the main political parties, including Muizzu's People's National Congress (PNC), are expected to make it hard for any single party to win an outright majority.
But Muizzu's prospects received a fillip with the release of his mentor Yameen from house arrest on Thursday.
A court in the capital Male ordered a retrial in the graft and money laundering cases that saw Yameen sent to prison after he lost a re-election bid in 2018.
Yameen had also backed closer alignment with Beijing while in power, but his conviction left him unable to contest last year's presidential poll himself.
He instead put forward Muizzu as a proxy, and after leaving the High Court, Yameen vowed to continue the anti-India campaign that helped his ally to victory.
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