Security is tight, with many areas still recovering after a northern rebellion and coup that resulted in foreign military intervention.
There are 27 candidates and if no outright winner emerges, the voting goes to a second round on August 11.
However, some analysts have questioned whether Mali is ready for the election.
Hundreds of thousands of people in the north were displaced by fighting. The majority of them will not be able to vote.
Islamist militants in the north have also warned Muslims not to take part and have threatened to attack polling stations.
There are also concerns about the fairness of the electoral process in the northern town of Kidal, which is still occupied by Tuareg rebels.
Tuareg gunmen were suspected of abducting electoral officials in the northern Tessalit area last week as they handed out voter identification cards. The officials were later released.
French troops are still deployed in the area with Chadian forces as part of the UN stabilization force, Minusma.
Despite the problems, Louis Michel, head of the EU’s election observer mission, said he was “positively surprised” by preparations for the vote and that the conditions were acceptable.
The US ambassador to Bamako, Mary Beth Leonard, said the fragility of Mali’s interim government had to end.
“A month ago, there were a lot of doubts [over the election]. But it has come together,” Mary Beth Leonard said.
Candidates include three former prime ministers, a former finance minister and one woman.
The frontrunners include Ibrahim Boubacar Keita, prime minister from 1994 to 2000, who founded his own party, the Rally for Mali (RPM), in 2001.
At his final rally in the capital Bamako on Friday, Ibrahim Boubacar Keita – known as IBK – appealed for a calm election day and vowed to ensure that “no-one will make fun of Mali again”.
IBK’s biggest rival is seen as Soumaila Cisse, who founded his own party, the Union for the Republic and Democracy (URD), in 2003.
Soumaila Cisse has called for the junta that seized power in 2012 to be cleared from the political scene.
Observers say Soumana Sacko, another former prime minister, can expect a good showing if there is no clear winner.
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