A police major in the southern Iraqi city of Basra put the toll from bombing at 20 killed and 15 wounded. A medic at Basra's Sadr Hospital said there were 25 dead and 40 wounded.
Both spoke on condition of anonymity.
The attacker, who had been distributing food to pilgrims walking to the Khutwa Imam Ali, a site on the outskirts of Basra venerated by believers for its associations with one of the key figures of their faith, blew himself up near a police checkpoint.
Pilgrims in south Iraq who cannot visit the central shrine city of Karbala to mark Arbaeen typically make the shorter trip to Khutwa Imam Ali, which lies around 12 kilometres (seven miles) west of Basra.
Arbaeen marks 40 days after the Ashura anniversary commemorating the slaying of Imam Hussein, one of Shiite Islam's most revered figures, by the armies of the caliph Yazid in 680 AD.