At least one bomber blew himself up outside the mausoleum of Sayid Mohammed bin Ali al-Hadi, which was then stormed by gunmen, reports say.
Another bomber is said to have blown himself up among fleeing worshippers.
Meanwhile the death toll from Sunday's suicide bombing in Baghdad has again been raised, from 281 to 292.
Amid growing public anger over the truck bombing, Iraqi Prime Minister Haider al-Abadi fired the three top security officials in Baghdad on Friday.
They were the head of Baghdad's security command, the head of interior ministry intelligence for Baghdad and the official responsible for Baghdad in the national security adviser's office.
IS said five of its members had carried out the raid on the site in Balad. The militant group follows an extreme form of Sunni Islam and often targets Shias, who it regards as apostates.
About 50 people were injured in the attack, police and medical sources said.
Islamic State: The full story
Worshippers were marking the Eid al-Fitr festival, celebrating the end of the Islamic holy month of Ramadan, when the site came under mortar fire.
The first bomber then struck a market at the entrance to the shrine.
A third bomber was shot dead before he was able to detonate his explosive vest, reports say.
It came four days after IS carried out the deadliest bombing in Baghdad, 45 miles (70km) south of Balad, since the 2003 US-led invasion.
That attack target a shopping complex in the mainly Shia Muslim district of Karrada.
IS militants overran large parts of northern and western Iraq two years ago, but government forces have since regained much of the territory.
In response to the battlefield setbacks, including the recent loss of the western city of Falluja, the militants have stepped up their attacks on civilians.
The Iraqi government has been accused of not doing enough to protect its citizens and has stepped-up security in Baghdad in response to the latest violence.

There were 69 claims against peacekeepers in 2015, up from 52 in 2014 was 66 in 2013.
Almost a third of the 2015 claims were made in the Central African Republic.
For the first time, the report has also set out all the countries whose soldiers are reportedly involved under a new "name-and-shame" policy.
Overall, 10 peacekeeping missions were subject to allegations in 2015.
The allegations involve military personnel, international police, other staff and volunteers.
According to the UN's latest figures, there are 124,746 personnel serving in 16 peacekeeping missions worldwide.
It has been criticised for failing to act quickly on sexual abuse allegations made against peacekeepers.
Last December an independent panel calling the UN response to allegations in the Central African Republic (CAR) "seriously flawed" and a "gross institutional failure".
It accused senior UN officials of abusing their authority by failing to take action over allegations of abuse by soldiers from France, Equatorial Guinea and Chad.
UN Secretary-General Ban Ki-Moon's report called for an international convention on "crimes committed in peacekeeping operations".
He also urged countries to change their laws so that they apply to sex crimes committed by citizens serving in UN peace operations.
Mr Ban also called for "on-site court martial proceedings" for some crimes and a DNA database of all peacekeepers.
UN peacekeepers operate under the legal jurisdiction of their home countries, making prosecution more difficult.
In February, the UN said it would send home more than 100 peacekeepers from CAR following sexual abuse allegations.
A 10,000-strong UN force took over a peacekeeping mission in the country in September 2014.
After CAR, the second highest number of allegations was at the UN peacekeeping mission in Congo, with 16 cases, followed by Haiti with nine.
Suicide bombers and gunmen have killed at least 35 people in an attack by so-called Islamic State (IS) at a Shia shrine in the Iraqi town of Balad.
[NEXT_CONCEPT]
Allegations of sexual exploitation or sexual abuse by United Nations peacekeepers rose by a third last year, according to a UN report.