Sadiq Zaman Khattak, a candidate for polls to a parliamentary seat in Karachi, and his son were attacked by gunmen as they were leaving a mosque in Bilal Colony after Friday prayers.
The attackers, who were riding a motorcycle, escaped after the shooting.
Officials said five persons were injured in the incident.
The banned Tehrik-e-Taliban Pakistan claimed responsibility for the attack.
Taliban spokesman Ihsanullah Ihsan was quoted by the website of Dawn newspaper as saying that his organisation was behind the attack on Khattak.
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The Election Commission announced the postponement of polls in the constituency where Khattak was contesting.
The shooting was the latest in a series of attacks by the Taliban targeting leaders and workers of the ANP.
Senior ANP leader Bashir Jan had a narrow escape in a recent bomb attack in Karachi that killed 11 people.
Scores of ANP workers have been killed in attacks by the Taliban in the country's northwest.
The party has curtailed its election campaign following the latest attacks.