Fellow candidate Osama al-Khafaji said the party had been concerned about harassment or verbal threats in the run-up to the elections.
"We are afraid that today's killing will not be the last," al-Khafaji said.
Police said party members had reported receiving a threat that four candidates from their list would be killed before Friday's attack.
Hillah, about 95 kilometres south of Baghdad, and other Shia cities in the south have been the site of fierce infighting among Shia parties for years as political groups jockeyed for power in the oil-rich south.
Tensions have been rising as the parties step up their campaigns for seats on the provincial councils.
US officials have pinned hopes on Iraq's first elections in just over three years to help unify the country's fractured ethnic and sectarian groups and solidify security gains.