Izzeddin al-Dolah's resignation marks the second high-profile Sunni departure from the government this month.
Fatal shootings have been comparatively rare during two months of anti-government rallies, and the protester's death is likely to heighten Sunni demonstrators' anger against the Shiite-led government.
The shooting happened in the city of Mosul, some 360 kilometers (225 miles) north of Baghdad, as angry protesters demanding the release of a local tribal sheik who was arrested earlier in the day, police officials said. Hospital officials confirmed the casualties. Both spoke anonymously as they were not authorized to speak to the press.
Al-Dolah linked his resignation to the shooting, saying the blood of those who voted for him is now being shed. Al-Dolah made the announcement at a news conference in Mosul, the capital of Ninevah province, where he is from.
"There is no way I can continue my work in a government that does not care about the demands of my people," al-Dolah said.
Al-Dolah is a member of the opposition Iraqiya bloc, which draws on Sunnis for much of its support. His announcement comes just weeks after Finance Minister Rafia al-Issawi announced his own resignation at an anti-government rally elsewhere in the country.
Minority Sunnis frustrated over what they claim is second-class treatment have taken to the streets across Iraq since late December.
In Baghdad, security forces prevented worshippers from holding Friday prayers at a prominent Sunni mosque in northern Baghdad, a cleric there said.
"This is sectarian escalation by the government that should listen to the people's demands instead of pushing the people to extremism," said Dawoud al-Alousi, the imam of Abu Hanifa mosque in the primarily Sunni neighborhood of Azamiyah.
Al-Alousi and witnesses said security forces blocked traffic on roads leading to the mosque. He said it was the first time that prayers at Abu Hanifa have been cancelled during the current unrest.
Meanwhile, demonstrators in the western cities of Fallujah and Ramadi blocked the main highway to Jordan and Syria to perform Friday prayesr. Others gathered in the northern city of Samarra.
Sunnis have staged mass protests since late December following the arrest of bodyguards assigned to a Sunni finance minister, the latest action by the Shiite-led government that Sunnis believe target prominent members of their sect.
In a previous incident on Jan. 25, security forces shot dead five demonstrators, but in general the protests and the security response have been less deadly than those in other Arab countries over the past two years.
Iraq also witnesses attacks by hardline Sunni insurgent groups, some of whom are believed to be trying to exploit anti-government anger to re-establish themselves in strongholds from which they were driven by U.S. forces and allied anti-al-Qaida Sunni militias in 2006 through 2008. Insurgents have often targeted members of those militias, known also as the Sahwa, whom they consider traitors.
Gunmen shot dead five Sahwa militiamen late Thursday after abducting them from their house south of Baghdad, police said on Friday.
The bodies of three brothers and their two cousins were found in a nearby orchard with bullets in their heads, they said.
Associated Press writer Adam Schreck contributed.