The governor was not near either blast.
The blasts occurred near several local government offices, Mohammed al-Mussawi, the head of the Karbala provincial council, told the Reuters news agency.
The attacks come days after Iraq's election commission announced complete results from the March 7 vote in which the Iraqiya party of Iyad Allawi, a former prime minister, narrowly edged out the State of Law bloc led by Nouri al-Maliki, the incumbent prime minister.
Allawi is pressing ahead with forming a government despite protests from al-Maliki against the outcome.
Iraqiya took 91 seats - two more than State of Law - in the final tally.
Allawi has said he hopes to form a government aligned with his secular principles.