A member of the security forces was also among those killed and least 34 people were wounded in the violence, according to government and medical spokespeople.
Shots fired after entering the Green Zone
The live rounds were said to have been fired close to the offices of Iraq's state broadcaster after protesters crossed the Al-Ahrar Bridge over the Tigris River.
The bridge separates Baghdad from government buildings in the high-security area, the so-called Green Zone.
Iraqi law enforcement had "dealt with" a group of protesters who set fire to a restaurant, after crossing a main bridge over the Tigris, according to a spokesman for the prime minister. He did not elaborate.
Security and medical sources confirmed the number of dead, but could only confirm that one death was from live fire, according to the Reuters news agency.
How many people have been killed so far?
The deaths came after three protesters were killed on Sunday night during an attack on the Iranian Consulate in Karbala, in southern Iraq.
Conservative estimates put the total number of people killed in anti-government protests at 250 since the beginning of October.