Polls opened at 8:00 am (local time) and were due to close at 0230 IST, with 23 million of the South American country's 30 million inhabitants called to cast ballots in the compulsory vote.
Half the candidates have dropped out or been excluded from the running under a tough new electoral law that saw Fujimori and other leading candidates accused of wooing voters with gifts.
The 40-year-old daughter of former leader Alberto Fujimori survived the charges and is likely to win about a third of the vote, according to three opinion polls published on Friday.
Fighting it out for second place are ex-prime minister and Wall Street banker Pedro Pablo Kuczynski, 77, and left-wing lawmaker Veronika Mendoza, 35.
Nine other candidates have either been excluded for irregularities or dropped out for lack of support. One, Gregorio Santos, is running for office from a jail cell where he is detained on corruption charges.
The leader of the Organization of American States, Luis Almagro, said the January electoral reform that allowed the candidates to be excluded risked turning it into a "semi-democratic election."
"I have a firm conviction that with God's help I will become the first woman president of Peru," she told thousands of supporters waving orange flags at her closing rally.
The Fujimoris are among thousands of families of Japanese descent who immigrated to Peru in search of a better economic future.
Alberto Fujimori, now 77, is in jail for crimes against humanity. The courts held him responsible for the massacre of 25 people he said were terrorists in 1991 and 1992.
"Her father was corrupt and a killer. She didn't do anything as a congresswoman. All she has is her family name."
But many voters praise Alberto Fujimori for crushing the Shining Path communist guerrilla group that carried out attacks and kidnappings.
"If Fujimori had continued as president, the country would be in a better state now," said taxi driver Felizardo Mogollon, 58.
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