Total turnout was 44.5% in the last election in 2018.
The electoral commission said early on Monday the lowest turnout was in Baghdad, with between 31% and 34%.
Two electoral commission officials told Reuters on Sunday that nationwide turnout of eligible voters was 19% by midday and participation was low at polling stations in several parts of the country.
Commission official Muhammad Mustafa said turnout picked up in the final hours of voting.
Results are expected on Monday at midday.
Iraqi elections are often followed by protracted talks over a president, a prime minister and a cabinet under the democratic system brought in by the 2003 US-led invasion.
The election was held several months early under a new law designed to help independent candidates - a response to widespread anti-government protests two years ago.
At least 167 parties and more than 3,200 candidates are competing for parliament's 329 seats, according to the election commission.