Some 4,900 legislators nationwide voted in what Modi termed a "historic" election to choose the titular head of state.
Modi's right-wing Bharatiya Janata Party (BJP) has nominated Ram Nath Kovind, a 71-year-old former lawyer from the Dalit community.
His main rival is Meira Kumar, the nominee of the Congress-led opposition and also a Dalit.
The result will be announced Thursday but Kovind's victory is almost certain since the BJP says it has the electoral college numbers needed to push its candidate through.
Members of both houses of the federal parliament and state assemblies across the country can take part in the vote.
"The presidential poll this time is historic. Probably for the first time no party has made any undignified or unwarranted comment on the rival candidate," Modi wrote on Twitter on the eve of the poll.
"Every political party has kept in mind the dignity of this election."
It is also historic as it will be the first time the BJP has organised the numerical strength to push through its candidate.
India's prime minister wields executive power, but the president can send back some parliamentary bills for reconsideration and also plays a guiding role in the process of forming governments.
- Modi ally - Analysts said Kovind's election will help Modi tighten his grip on power and accrue political capital by sending an important message to the Dalits, a long-disdained electoral group once known as "untouchables".
It will be only the second time that India has had a Dalit head of state.
Dalits, who number around 200 million in the nation of 1.3 billion, are among India's poorest communities and relegated to the margins of society.
Despite legal protection, discrimination is rife and Dalits are routinely denied access to education and other advancement opportunities.
On the day of the vote, media reported the case of a Dalit labourer allegedly beaten to death by upper-caste attackers, highlighting the plight of the "untouchable" caste.
Modi's rivals have protested at Kovind's nomination, citing his association with the radical right-wing Rashtriya Swayamsevak Sangh, the ideological power behind the BJP.
The opposition nominee Kumar, the daughter of freedom fighter Babu Jagjivan Ram, was a diplomat before entering politics in 1985 and became India's first woman speaker in 2009.
Her nomination, which followed Kovind's, was seen by many as an opposition attempt to counter Modi's move to woo Dalits.
Congress president Sonia Gandhi rallied opposition ranks before the vote, calling the contest a "clash of ideas and a conflict of disparate values".
"We cannot and must not let India be hostage to those who wish to impose upon it a narrow-minded, divisive and communal vision," Gandhi said.
Votes from the BJP's traditional Hindu base propelled Modi to his 2014 landslide general election victory, especially in the battleground states of Uttar Pradesh and Bihar.
Dalit support will be key for the BJP before the 2019 general election as the party has been largely shunned by Muslims, who make up about 14 percent of the population.
Indian Prime Minister Narendra Modi leaves after casting his vote to elect President at Parliament House in New Delhi.
Indian lawmakers voted Monday to pick the country's president, who is certain to come from the lowest Dalit caste, in an election seen as strengthening Prime Minister Narendra Modi's grip on power.
