At least four people, including a police officer, were wounded on Thursday.
The protesters demanded the resignation of the deputy governor and police chief because they think their clan was responsible for Wednesday's killing of Ali Ghalib Ibrahim, who belongs to a rival clan, Mayor Wael Ibrahim Ali said.
Ibrahim, who led Salahuddin's provincial council, was killed while driving in Tikrit, the province's capital, 130km north of Baghdad.
He was fighting the corruption in the city council, and that's why they assassinated him," Ali said during the demonstration.
Police guarding the provincial government building first fired warning shots into the air followed by volleys into the crowd, police Lieutenant Khudhir Ali said. The four wounded included a police officer, but it was not clear how he was shot, he said.
Reuters camera operator Amer Salman said armed men were among the crowd of demonstrators that clashed with police.
Mortar attacks aimed at a police station killed four civilians and wounded up to 46 more after striking surrounding streets in Mosul, the US military said.
US convoy attacked
A roadside bomb has struck a US military convoy in eastern Baghdad, wounding two soldiers.
The blast early on Thursday caused a Humvee to slide off the road and flip over into a canal, said Sergeant 1st Class David Abrams, a spokesman for Task Force Baghdad.
The wounded soldiers were evacuated for treatment, he added.
The attack occurred at about 7.30am (0330 GMT) in the Sadr City neighbourhood.
Separately, five decapitated bodies were found on Thursday on a road in northwestern Iraq, police said. The bodies were dressed in civilian clothes and found on the road between Rawah and Ramadi, police Major Hashim Mohammed said.
Rawah is 210km northwest of Ramadi, the capital of Anbar province.