At least 17 protesters were wounded, including six with bullet wounds, the source said.
The young demonstrators have mostly thrown rocks at riot police but some have tossed Molotov cocktails.
In Nasiriyah to the south, security forces also fired live rounds but there was no immediate word on casualties.
The protests erupted in Baghdad and the Shiite-majority south on October 1.
This happened in outrage over lack of jobs, poor services and rampant corruption.
Met with violence, they quickly spiraled into calls for a total government overhaul.
Rallies are now specifically demanding snap elections.
The appointment of an independent premier and the prosecution of anyone implicated in corruption or the recent bloodshed were among the demands.
