The Sunday's vote came hours after the violence-hit West African country announced its first coronavirus death and days after main opposition leader Soumaila Cisse was kidnapped by unidentified gunmen.
The vote will see new MPs elected to the 147-seat National Assembly for the first time since 2013, when President Ibrahim Boubacar Keita's Rally for Mali party won a substantial majority.
Parliamentary elections were meant to take place again in late 2018 following Keita's re-election, but the poll was postponed several times, largely due to security concerns.
After Sunday's first-round vote, a second round is scheduled for April 19.
Late on Saturday, just hours before polls were scheduled to open on Sunday, the country's first coronavirus death was announced, with the number of infections rising to 18.
Some 200,000 people displaced by the near-daily violence in Mali's centre and north will not be able to vote, because "no mechanism has been established" for them to do so, a government official said.
There were security fears about the vote even before the African country recorded its first coronavirus infection on Wednesday amid concerns that the impoverished state of some 19 million people - where large swaths of territory lie outside state control - is particularly exposed to a COVID-19 outbreak.
"There's a state of emergency both because of the threat of armed groups and the threat of coronavirus," Al Jazeera's Nicolas Haque, who has reported extensively on Mali, said.
"Still, Keita on Wednesday said these elections need to go ahead, that they were essential for Mali to head towards peace and national dialogue."
The government's election spokesman, Amini Belko Maiga, has admitted that voting conditions were not ideal.
"It's true that we cannot say that everything is perfect, but we're doing the maximum," he said, referring to the threat of coronavirus. He added that hand-washing kits had been distributed in the countryside, while in the capital, Bamako, authorities would make masks and hand sanitisers available.