The law, backed by some Shia leaders who have been keen to set up a big, autonomous region in their oil-rich south, was passed in a session of parliament on Tuesday.
The vote was boycotted by the Accordance Front, the largest political bloc of the Sunni Arabs.
Hostility between rival political parties over federalism - one of post-war Iraq's most sensitive issues - is threatening the ability of the four-month-old national unity government to rein in mounting sectarian and ethnic violence.
Legislators loyal to Muqtada al-Sadr, a populist and radical Shia leader, and the smaller Shia Fadila party stayed away from Wednesday's vote, showing Shia support for federalism is not unanimous.
Shia and Sunni leaders last month agreed to put off implementation of the federalism law for at least 18 months, effectively delaying the creation of any autonomous regions until 2008.
Iraq's Sunni Arabs fear that a federal Iraq would hand northern and southern oilfields to ethnic Kurds and Shia loyal to Iran respectively.
The biggest Shia party, SCIRI, proposes merging nine of Iraq's 18 provinces into one autonomous region in the mostly Shia south.
Sunnis want amendments to the constitution that keep the wealth distribution power in the hands of the central government.