Chaudhry Zulfiqar was shot multiple times after gunmen intercepted his vehicle after he left home. His bodyguard was also wounded and a woman passer-by killed.
President Asif Ali Zardari, Bhutto's widower, condemned the killing and ordered a thorough investigation to "expose the real culprits involved in the murder", his office said.
In other event, a candidate running for parliament in next week's historic Pakistani election was also shot dead along with his three-year-old son after praying in a mosque in Karachi.
Saddiq Zaman Khattak was a businessman and a candidate for the Awami National Party (ANP), the leading secular party in Pakistan's ethnic Pastun northwest. A party leader said he had previously received threats.
"He was returning from a mosque after saying his Friday prayers with his three-year-old son when gunmen on a motorbike opened fire. Both were killed," police spokesman Imran Shaukat told AFP.
Pakistani Taliban claimed responsibility for the attack and threatened further attacks on the ANP and its outgoing coalition partners, the Pakistan People's Party and MQM, the main party in Karachi.
Karachi has seen a string of attacks on the election campaign.
Late Thursday, a bomb wounded at least five people near an election office for MQM, the party that dominates Karachi.
Three bombs, two of which targeted MQM and the Pakistan People’s Party (PPP), killed three people and wounded 49 others on Saturday.