The vote pits incumbent Danilo Turk against former PM Borut Pahor, who is favored to win by opinion polls.
On Friday, a number of people were injured as protesters clashed with police in the capital Ljubljana.
Slovenia is facing one of the deepest recessions among the 17 countries in the eurozone.
The country’s economy has shrunk more than 8% since 2009.
Thirty-three people were charged with public order offences after the trouble in Ljubljana, police said.
A protest that attracted thousands of people earlier in the week in the second city, Maribor, also turned violent.
Polls across Slovenia are due to open at 07:00 local time and close at 19:00 with first results expected within hours.
Borut Pahor won the first round of the election, and recent opinion polls suggest the ex-PM will be triumphant again on Sunday.
Commenting on the recent protests in the country, Borut Pahor told the Associated Press that the demonstrations “signal a lack of confidence” in government institutions.
Many protesters are angry at what they describe as harsh austerity measures being implemented by the current centre-right government.
They also accuse the government of corruption – a claim denied by the authorities.
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