The rocket attacks targeted Shiite worshippers in the northwestern town who were marking the end of the holy festival, authorities told Iran's Press TV.
CNN reported an estimated 2 million pilgrims were expected to gather in Karbala to mark the religious festival, leading to an increased military presence in the area.
Ashura marks the killing of Imam Hussein, grandson of the Prophet Muhammad, in 680 A.D.
The Washington Post reported Ashura ceremonies in the past have been targeted by Sunni insurgents, including an attack Friday that left more than 40 people dead in Nasiriya and Basra.
Iran's Press TV said that prior to Saturday's deadly attack, two people were killed and another seven were injured in the city of Kirkuk when a roadside bomb detonated.
Putin thinks Obama would save him if he were drowning
Justin Bieber crashes Drake Bell's album release party