The current prime minister is Andrus Ansip, the Reform party leader.
In a system of advance voting, more than 30,000 people including Ansip voted online earlier in the week. Its aim was to make voting easier and encourage more people to vote.
Estonia became the first country in the world to have voted online for parliamentary polls.
The country has some of the worst health statistics, including high rates of alcoholism, HIV infections and traffic-related deaths, among the EU.
Rampant inflation has forced the government to postpone plans to adopt the EU's common currency while a westward flow of skilled workers has led to a labour shortage. Companies ranging from shipyards to software makers such as eBay-owned telephony company Skype have had to import workers from countries such as Ukraine and India.
The run-up to the election was overshadowed by a dispute over a Soviet monument in Tallinn that has exposed divisions between ethnic Estonians and the country's Russian-speaking minority, which makes up about one-third of the population.
Ansip has called for removing the Bronze Soldier monument and war grave, which Russians see as a tribute to the Red Army's victory over Nazi Germany, but which many Estonians consider a painful reminder of five decades of Soviet oppression.