"Eleven dead have been received," Seemi Jamali, senior medical officer at Karachi's Jinnah Hospital, told reporters.
Women and children were among the dead, he said. Another 32 people were injured.
The first blast occurred at 9.00am, an hour after voting began, in front of the secular Awami National Party's election office in Karachi's Quaidabad district and nearly destroyed the office.
The bomb was planted in a motorized rickshaw which had been parked in front of the ANP office, police said. A polling station was just 500 metres away.
The second bomb exploded 45 minutes later about two kilometers from the ANP office. Several ANP party workers were among the dead and injured, ANP leader Bashir Jan told reporters.
ANP candidate Amanullah Mehsud was the target of the attack and was in the office at the time but was not injured, Jan said.
"It was an attack on Amanullah Mehsud, but he escaped unhurt," Jan said.
The lead-up to Saturday's elections for the national and provincial parliaments has been bloodied by a string of deadly bomb attacks.
Taliban militants had vowed to disrupt the polls and pledged to target the ANP, the Pakistan People's Party and the Muttahida Qaumi Movement because they are secular parties.
Campaign events and party offices were hit in at least nine bomb attacks across Karachi between April 23 and May 3. The outlawed Tehreek-e-Taliban Pakistan militant group is blamed for the pre-election attacks, in which more than 31 political activists were killed and 161 injured. While violence has long been a feature of elections in Karachi, observers had expressed concern about the wave of attacks in the lead-up to polling day.
Tehreek-e-Taliban was "taking advantage of ethnic, political and gang-war violence," in the crowded port city, Zia Ur Rehman, a Karachi-based security analyst, told UPI Next.