Armed men burst into the house of the leader of a government-allied militia on Sunday and fatally shot him and his wife, police told the German Press Agency dpa.
"Gunmen broke into the house of Sheikh Karim Abdullah al-Luhaibi, the head of the Awakening council of al-Karama region, and shot him and his wife," a police spokesman said.
Iraqi and US officials credit the Awakening, or "Sahwa", militias with helping to restore order in the mostly Sunni areas they have patrolled since 2007. The militiamen, some of whom were insurgents, have frequently become targets for assassination.
Falluja, formerly the site of some of the worst fighting between insurgents and US and Iraqi forces, lies roughly 60 kilometres west of the capital, Baghdad.
Tensions are high in Iraq as poll workers continue to count the votes from the parliamentary elections.
The March 7 polls have been seen as a key test of Iraq's stability ahead of US combat troops' withdrawal from the country by the end of the year. Top US officials have tied US soldiers' withdrawal from Iraq to a period of calm following the elections.