One of the wounded was Shaikh Abd al-Mahdi al-Karbalai, a cleric regarded as close to Ayat Allah Ali al-Sistani, Iraq's most influential Shia leader.
Hospital sources said al-Karbalai, near whose office the blast occurred, had been hit in the legs and was receiving treatment.
The attack on Wednesday came as campaigning began for Iraq's 30 January elections.
One of the groups contesting the poll is a list of mainly Shia candidates backed by al-Sistani, but it was not immediately clear if there was any political motive for the bombing.
No one immediately claimed responsibility for the attack.
At least four of those killed worked as guards in al-Karbalai's office, hospital sources said. The wounded were mostly office staff and passers-by.
The office is in the centre of Karbala, close to the shrine of Imam Hussein, one of the holiest sites in Shia Islam.
It was the first major attack in the city after a period of calm following clashes that erupted between US-led forces and supporters of Shia cleric Muqtada al-Sadr.