Ali Haider, 27, was on his way to an election rally in Mati area of Multan, 350-km from Lahore, when the gunmen intercepted his SUV and fired indiscriminately.
The gunmen, who came to the spot on a motorcycle and a car, took Ali Haider away with them, said Iftikhar Baloch, a close associate of the former premier.
Mohiyuddin, the personal secretary of Ali Haider, was killed and four bodyguards were injured, Baloch told PTI.
Ali Haider, who was campaigning for his elder brother Abdul Qadir, is one of a set of triplets.
Gilani, who has four sons and a daughter, is one of the top leaders of the Pakistan People's Party, which led the outgoing government.
No group claimed responsibility for the abduction.
Punjab Police blocked all entry points of Multan as part of efforts to trace Ali Haider.
Former Interior Minister Rehman Malik told PTI that he did not have any information about the involvement of the Pakistani Taliban in the kidnapping. "However, I cannot rule out the hand of extremists in this incident," he said.
The former premier has also refused to lead PPP election rallies because of a threat from the banned Tehrik-e-Taliban Pakistan.
Tehrik-e-Taliban Pakistan has warned it will target secular parties like the Pakistan People's Party and Awami National Party ahead of the May 11 general election.
The threats have forced the parties to virtually stop campaigning for the polls. The elections mark a historic milestone for the nation as one civilian government completes its term and prepares to hand off to another.
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