Opinion polls have shown comedian Volodymyr Zelenskiy is leading the field.
Ukrainians are casting ballots in a presidential election that follows a campaign marred by vicious political infighting and allegations of bribing of voters.
The nation of 42 million people will choose from among 39 candidates it hopes can guide the country out of troubles including endemic corruption, a seemingly intractable conflict with Russia-backed separatists in the country’s east and a struggling economy.
Opinion polls have shown comedian Volodymyr Zelenskiy leading the field with President Petro Poroshenko and former prime minister Yulia Tymoshenko trailing behind by a broad margin.
If none of the candidates gets an absolute majority of the vote, a run-off between the top two will be held on April 21.
Concern about the election’s fairness spiked this week after the interior minister said his department was “showered” by hundreds of claims that campaigners for Mr Poroshenko and Ms Tymoshenko were offering money in exchange for votes for their candidates.
Mr Poroshenko, a confectionery tycoon whose popularity has sunk amid Ukraine’s economic woes and a sharp plunge in living standards, has been accused of turning a blind eye to corruption.
Ultra-right activists have shadowed him throughout the campaign, demanding the jailing of Mr Poroshenko’s associates who are accused of involvement in a military embezzlement scheme.
Like his famous character, a schoolteacher who becomes president after a video of him denouncing corruption goes viral, Mr Zelenskiy has focused strongly on corruption, proposing a lifetime ban on holding public office for anyone convicted.
He also called for direct negotiation with Russia on ending the conflict in eastern Ukraine.
Ms Tymoshenko has played heavily to the economic distress of millions of Ukrainians, denouncing the price hikes introduced by Mr Poroshenko as “economic genocide” and promising to reduce prices for household gas by 50% within a month of taking office.
The incumbent shot back at his rivals, describing them as puppets of self-exiled billionaire businessman Ihor Kolomoyskyi, who lives in Israel. Mr Zelenskiy and Ms Tymoshenko have rejected those claims.
Many political observers have described Ukraine’s election campaign as a battle between Mr Kolomoyskyi and Mr Poroshenko, who was on Forbes Magazine’s list of billionaires in 2014 before dropping off the following year.
Both the president and Mr Kolomoyskyi have relied on an arsenal of media outlets under their control to exchange blows. Just days before the vote, Mr Kolomoyskyi’s TV channel aired a new season of the Servant Of The People” TV series starring Mr Zelenskiy as Ukraine’s leader.