The main opposition candidates, Pascal Affi N’Guessan and Henri Konan Bédié, say it is illegal for Mr. Alassane Ouattara to stand for a third term.
At least 30 people have been killed in pre-election violence, evoking memories of a 2010-11 crisis that killed about 3,000 people.
Polling stations opened at 8am (08:00 GMT) and will close at 6pm (18:00 GMT).
The opposition leaders called for an election boycott and civil disobedience, though they have not formally withdrawn their candidacies.
The fourth challenger is independent candidate Kouadio Konan Bertin.
Ouattara, 78, was supposed to step aside after his second term to make way for a younger generation, but the sudden death of his chosen successor forced a change in plan.
The Ivorian leader, a former IMF official who has been in power since 2010, says a Constitutional Court ruling approved his third term, allowing him to bypass two-term presidential limits after a 2016 legal reform.
But Bedie and opposition leaders say a third mandate is unconstitutional.
They accuse the electoral commission and the Constitutional Court of favouring the government, making a fair and transparent vote impossible.
The African Stand’s Esther Kamara reporting from the Nigerian capital, Abuja said the vote is not expected to bring Ivorians together.
“Looking at the history of elections in Ivory Coast, many people in the country believe the opposition will stand firm on their word that civil disobedience against Ouattara and the election will continue. This is what many fear and it could lead to violence,” Idris said.
Protesters on Saturday blocked the main route between Abidjan and the north of the country near the central town of Djebonoua, 350 km (220 miles) north of Abidjan, local residents said.
Groups of youths also set up makeshift barricades in some neighbourhoods in and around Daoukro, a stronghold of opposition leader Bedie, AFP news agency reported. In Benanou, a village near Daoukro, a large tree trunk blocked a key road.
The United Nations has urged calm, but the opposition called for a campaign of civil disobedience to stop the vote, stoking fears of more violence in opposition strongholds.
More than 35,000 police and security personnel have been mobilised to secure the election.
The run-up to the polls saw sporadic clashes in the south of the country, mainly between local ethnic groups close to the opposition and Diaolu communities from the north who are seen as loyal to the president.
The country’s political feuds are often closely tied up with its leader’s ethnic identities and regional loyalties.
On Friday, police fired tear gas in the political capital of Yamoussoukro to break up fighting between Diaolu youth and opposition-aligned Baoule communities, according to residents.
Under the constitution, the electoral commission has five days to announce the results.