Thursday's attack came less than three weeks before a nationwide poll on March 7, which would be only the second parliamentary election held since the 2003 US-led invasion.
Mohammed Dulaimi, the owner of a restaurant that was badly damaged in the blast, said the attackers were "trying to undermine the political process and prevent us from taking part in the election".
"They want us to miss the opportunity to vote, as we did before," he said, referring to a boycott of 2005 general elections by Sunni-led political parties.
Anbar province was considered a stronghold of anti-government fighters in 2005 and 2006, but support for them apparently dried up following civilian deaths and after US and Iraqi authorities forged alliances with Sunni tribal leaders to form so-called Awakening councils.
Next month's poll is being seen as a crucial test for the country, and for reconciliation between Sunni and Shia factions, after more than seven years of bloodshed and sectarian strife.