Polls have opened in Ukraine's presidential election that pits the incumbent against a popular comedian and a former prime minister.

Ukrainians on Sunday will choose from among 39 candidates they hope can guide their country of more than 42 million 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, who plays the country's president in a popular TV series, 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 runoff between the top two will be held on April 21.