Faris Naser Husain was killed and his colleague Haydar Kasim Shinshu was wounded as the two MPs with the Kurdish list in parliament were heading towards Baghdad.
A driver and bodyguard were also killed in the attack, near Mushahada, 30km north of the capital, an Interior Ministry official said on Sunday.
Husain is the third lawmaker to be killed since the January elections.
Seventy-five of parliament's 275 members were elected on the Kurdish list, which includes Sunni Arabs, Turkmen and other minorities living in Kurdish regions, and supports the government.
Parliament was meeting on Sunday to sign the final amendments to the draft constitution which will be put to a nationwide referendum on 15 October.
Deputy Speaker Hussein Sharistani was due to read the amendments to parliament which would then be automatically deemed approved.
The text of the draft will then be sent to the United Nations which is to print five million copies for distribution to the public ahead of the referendum.
US soldier killed
A US soldier was killed by a bomb explosion on Saturday near al-Asad, in western Iraq, the US military said in a statement on Sunday.
His death brings to at least 1899 the number of American military personnel killed in Iraq since the US-led invasion of March 2003, according to Pentagon figures.
The death also comes as Iraqi PM Ibrahim al-Jaafari told the UN General Assembly in New York that it was not yet time for the departure of the US-led forces from the country.
Meanwhile, Aljazeera has reported that unidentified fighters are believed to have taken 15 Iraqi soldiers hostage west of Samara.
Aljazeera also reports that the al-Qaida leader in Mosul, Junaid Farhat, has been killed in a US airstrike - along with four of his men.
In Baghdad, unidentified fighters set off a blaze when they blew up a train carrying petroleum products early on Sunday, the second such attack in less than two months, an interior ministry official said.
"Two tankers are on fire and firemen are trying to put out the blaze," the official said, adding that the attack took place in the capital's southern district of Dora, near an oil refinery.
There were no reported casualties.
In a separate development, angry Shia militiamen took to the streets of the southern Iraqi city of Basra on Sunday after British soldiers and police arrested their local leader, Iraqi army and Shia officials said.
Attacks against British forces
have increased in Basra
Dozens of militiamen from Shia cleric Muqtada al-Sadr's outlawed Jaish al-Mahdi (al-Mahdi Army) gathered around the local al-Sadr office.
Iraqi army officials said British soldiers and riot police on Saturday raided the home of local al-Mahdi Army leader Shaikh Ahmad al-Fartusi, arresting him, his brother and an unidentified third man.
There was no immediate comment from British forces in the area, although a spokesman confirmed that "an operation took place earlier".
There has recently been an increase in attacks against British and coalition forces in the area where three British soldiers have been killed in bomb explosions.