Attackers planted several bombs inside the shrine to Imam Askar between the towns of Balad Ruz and Mandalay on Friday morning. The resulting explosion destroyed the monument.
West of the shrine, in a small village in the Imam Ways region, gunmen in a car opened fire on three brothers from a Shia family, killing them all.
Three people were also killed south of the relatively stable city of Kirkuk when a roadside bomb destroyed their car.
East of Kirkuk, in Hawija, which has been a focus for the insurgency, a policeman and a bystander were shot dead in an attack aimed at a passing police patrol.
Gunmen also killed an Iraqi soldier in the nearby village of Riyadh, and kidnapped a Kurdish security guard in Kirkuk itself.
In the oil refining town of Baiji, in the centre of the country, a train station official was shot dead by gunmen.
In Tikrit, the birthplace of former president Saddam Hussein south of Baiji, two Iraqis were killed outside their house.
South of Baghdad, in the Babil province, police reported clashes between the Shia Mehdi Army militia of Moqtada al-Sadr and US forces. A curfew was placed on the town after the fighting.
Sources within the militia said that one of their members was killed by US forces and one wounded.
In Baghdad three people were killed when a mortar bomb struck a Sunni mosque in the southern outskirts of Baghdad.
An influential Shia leader has said that Iraqis should handle their own security affairs said that foreign interference was stopping them from catching terrorists.
Abdel Aziz Hakim, leader of the Supreme Council for the Islamic Revolution in Iraq (SCIRI), said that "the security file should be handed over to Iraqi forces and no one should interfere with it."
Hakim was speaking at a ceremony commemorating the anniversary of the assassination of his brother, Mohammed Baqr al-Hakim, three years ago.
Many members of SCIRI's former militia, the Badr Organization, have joined security forces and have been accused of sectarian-linked human rights abuses.
Hakim called for militias to be disbanded and the "root causes" behind their formation to be addressed. He also encouraged further arming of people to protect themselves.