It was not immediately clear who was behind the shelling in various areas in the south of city, just a short drive to the west of Baghdad.
The bombardment began yesterday night and continued today, Doctor Ahmed Shami said, adding that four people were also wounded.
In a sign of both the reach of anti-government militants and the weakness of security forces, all of Fallujah and shifting parts of Anbar provincial capital Ramadi, farther west, have been out of government control since early January.
Militants subsequently seized parts of Ramadi and all of Fallujah, the first time anti-government forces have exercised such open control in major cities since the peak of the deadly violence that followed the US-led invasion of 2003.
The bloodshed comes during vote counting from the April 30 general election, the first since American troops withdrew in late 2011, and amid a protracted surge in nationwide unrest.