At Baghdad's Yarmuk hospital on Monday, election officials said the first of 1500 patients began voting. Voting should end at 5pm.
On Tuesday, the estimated 1.5 million Iraqi voters living outside the country can begin casting their ballots at polling centres in 15 countries, including the US, Canada and Australia.
Voting also ends on Thursday evening in each of these countries.
"The election process is running very well," said Yousif Ibrahim, director of the election centre.
"There is a big hall for patients who can easily walk and the election committee moves a box around to the wards where there are patients who can not leave their beds."
Draconian security measures, similar to those enforced during two earlier elections this year, have been imposed to keep attacks at bay and minimise bloodshed during Thursday's main event.
Airports and borders will shut from Wednesday until Friday or Saturday, curfews extended and a ban on carrying weapons imposed even for those with permits. A five-day public holiday will also be in effect.
Success of the election hinge on
turnout among Sunni Arabs
"We are hoping for a calm day as during the referendum," said Interior Minister Bayan Jabr Solagh.
A vote on the country's new constitution on 15 October passed without the spectacular bombings that have become post-invasion Iraq's trademark.
Monday's special polling booths opened at 7am (0400 GMT) and were to close at 5pm (1400 GMT), electoral official Farid Ayar confirmed.
In the northern Kurdish city of Sulaymaniya, 19,800 hospital patients, detainees and security forces had registered to vote in 499 special polling booths, said Shaikh Latif, a local electoral commission official.
This week's election marks a new beginning for Iraq following the chaos that prevailed after the removal of Saddam Hussein by US-led invasion in 2003, two transitional governments and the adoption of a constitution in October.
When the dust settles on the inevitable political horse trading, Iraqis will be left with a four-year parliament to carve out a new direction for the country, which is teetering on the tightrope of inter-communal tensions.
Moves towards democracy, marked by well-organised ballots and determined turnout, are a cornerstone of US policy in the Middle East, with Washington increasingly focused on an ultimate exit strategy from Iraq.
But the success of the election and future prospects of stability hinge on the turnout among the Sunnis who boycotted the January 30 election for a transitional parliament.
"The election process is running very well"
Iraqi election centre director
Iraq's 15.5 million voters will elect a 275-member assembly from about 7000 candidates in the first full-term legislature since the invasion of Iraq in March 2003.
The 228 political entities that have presented candidates are roughly double the 111 groups that contested in the initial poll in January.
The first task of MPs will be to appoint, by a two-thirds majority, a president and two vice-presidents.
The presidency council will then have 15 days to name a prime minister, who will form a cabinet to be put to parliament for approval.