Except for a few stray incidents, officials said the elections went peacefully.
Police said three mortar shells landed in Tikrit after polling stations opened. No casualties were reported, but a vehicle was reportedly set on fire.
Results from Saturday's elections are not expected for several days.
Iraq's provincial councils are responsible for nominating the governors who lead the administration, and oversee finance and reconstruction projects. They control a combined budget of $2.4bn.
"I hope that the results will lead to new provincial councils that work for the interests of citizens," Hashem Karim, a voter waiting in a queue at a polling station in Nasiriyah, said.
Al Jazeera's Anita McNaught, reporting earlier in the day from a polling station in Irbil, in northern Iraq, said voting was going smoothly.
"Reports we're getting from the rest of the country indicate that pretty much things are going well. There hasn't been an uptake in violence, as people were fearing," she said.
"One interesting bit of news coming through - we've heard that Iraqi security forces have intercepted some boxes of fraudulent votes they found being taken into the Salahuddin province region, near the area of Tikrit."
Elections are not taking place in the three autonomous Kurdish provinces, Irbil, Dohuk and Sulaimaniyah, until later in the year.
However, because a large numbers of Iraqis have fled their homes due to violence or sectarian threats, the election commission set up polling stations in the Kurdish north to allow those registered further south to cast a vote in their home constituencies.
Polls in the oil-rich Kirkuk province, which the Kurds want to incorporate into their region despite fierce opposition by the central government, have been postponed indefinitely.
The killing of three Sunni Arabs candidates on Thursday, and that of a Shia politician two weeks earlier, had raised fears of violence on election day.
Iraqi and US military commanders in recent days also warned that al-Qaeda poses a threat to the elections, and the US military said it was sending heavy deployments of troops onto the streets during the voting.
Hundreds of women, including teachers and civic workers, have been recruited to search female voters after a rise in female suicide bombers last year.
Almost 300,000 local and international observers monitored the elections.
Staffan de Mistura, the UN special envoy to Iraq, visited a voting stations in Ramadi, the capital of Anbar province, and said that "the people look quite [well] trained, and the proper procedures were being applied".
Elections were held in 14 of total 18 provinces
About 15 million Iraqis were eligible to vote
There were 5 major parties to choose from
More than 14,000 candidates contested the polls
Campaign rules prohibited the use of government resources and gifts to voters, and restricted the use of religious symbols.
The independent electoral commission said it had received very few complaints about attempts of vote buying, but the issue has become a talking point among Iraqis.
Qassim al-Aboudi, a representative of the electoral commission, said it had fined three political lists for campaign violations, but he declined to identify them or their misdemeanours.
"We received very few reports about attempts to buy votes and we will take action against these parties," he said.
In a Baghdad park this week, a leading Shia party distributed blankets with a pamphlet inserted in the folds instructing voters which candidates to choose.
Other parties have reportedly given out watches to win favour, and in one case, equipped a teenage football team with uniforms.
Nuri al-Maliki, the prime minister, rejected media reports about attempted vote fraud.
"We want to show the world our elections are transparent," he said.
Mithal al-Alusi, a parliamentarian who heads a secular list of candidates, accused some parties of misusing state funds.