ISIS' media wing, Amaq, claimed responsibility for the attack.
Amaq said the attackers clashed with security forces for several hours, later detonating their suicide vests to target Iraqi security forces. CNN could not independently verify the claim.
While security forces were successful in stopping five of the bombers, one managed to enter a house and detonate his vest, killing six people and injuring six more.
Separately, two suicide car bombs killed at least nine people in the city of Falluja on Monday, according to municipal health and security officials.
The dead included at least two police officers, and 25 people were wounded in the blasts. One car bomb exploded at a security checkpoint in the al Risala neighborhood, and the second attack occurred at a security checkpoint in the al Nazal neighborhood.
Amaq also claimed responsibility for the attacks in a statement published on Twitter. The bomb attacks are the first in the city since government forces retook it from ISIS in June.
Ain Al-Tamur, where the suicide bomber attacked, is a small, historic town about 45 km (28 miles) west of Karbala. It's famous for its springs and ruins, according to Lt. Ali Qassim, a police official there.
It is a predominately Shiite village and in August was again a target for ISIS attacks that killed more than 18 people, Qasim added.
Every year, hundreds of thousands of pilgrims amass in Karbala for al-Arbaeen, which commemorates the end of a 40-day mourning period for Imam Hussein, the grandson of the Prophet Mohammed.
He died in battle in the 7th century, and is buried in Karbala, about 60 miles southwest of Baghdad. Karbala's main holy site is the gold-domed Imam Hussein Shrine.
Tried and tested strategy
Suicide bombs have long been an ISIS mode of attack. Two days ago, a suicide bomb attack killed at least 52 people
and injured more than 100 others during a religious ceremony in the Lasbela district of Balochistan, according to local law enforcement.
Again through its media wing Amaq, ISIS claimed responsibility for the Saturday evening blast on a Sufi shrine, 120 miles from Karachi.
, three separate attacks on one day in Baghdad killed at least 15 people.
It is also a common strategy in the group's defense of the city of Mosul, which it has occupied since 2014. The city is the subject of a concerted push by Iraqi forces to liberate it from the jihadists.
Mosul: Gains made
On Sunday, Iraqi forces liberated the village of Nimrud
and the site of the ruins as part of the ongoing battle for Mosul, ISIS' last major stronghold in Iraq, according to Col. Mohammed Ibrahim, a spokesman for Iraq's Joint operations command.
ISIS is fortifying positions in eastern Mosul, digging new trenches, building berms and erecting walls and barriers on major roads, witnesses and residents tell CNN. They say the terror group has also rigged farm equipment with explosives and hid them in residential areas of several neighborhoods.
Intense clashes between ISIS and Iraqi forces lasted for several hours Sunday in the eastern neighborhood of Al Intisar, residents there say.
Iraqi forces have been slowly battling their way towards the center of Mosul, encountering fierce resistance. In the Al Zahraa neighborhood, they are using abandoned cars left behind by fleeing citizens to block roads against ISIS car bombs.
Much-needed food supplies arrived in parts of Mosul Sunday. CNN saw 20 trucks with white flags and carrying World Food Program boxes at the eastern entrance of the city. Other witnesses saw food and first aid supplies arrive in Al Zahraa.