The parliamentarian, Ahmed al-Awlani, was wanted on terrorism charges, the BBC reported.
Eighteen people were wounded when Awlani's guards opened fire as troops and police special forces arrived at Alwani's home in Ramadi, RTT News reported.
The reason for his arrest was not immediately clear.
Awlani is a prominent backer of a group of Sunni activists who have set up a camp on a highway outside Ramadi to protest what they call Prime Minister Nouri al-Maliki's persecution of the Sunni minority.
More than 8,000 have died this year in violence between Shiite and Sunni Muslims.