The remote-controlled blast occurred outside a crowded restaurant in the Hub industrial area, which links Karachi with Balochistan, as a vehicle carrying Salman Mamnoon passed by late last night.
Salman, who was apparently the target of the attack, escaped unhurt while three passers-by, including a child, were killed.
Salman's vehicle had already passed the spot where the improvised explosive device (IED) exploded, hitting a rickshaw and the last vehicle of the convoy.
Seven policemen and eight others were also injured in the explosion. The vehicle the policemen were travelling in was partially damaged.
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"The explosives were planted in a motorcycle parked near the restaurant and apparently the militants knew the President's son Salman would pass through on the road as he frequently goes to Hub industrial area where he has a farming business," an official told PTI.
Superintendent of Police, Hub, Jam Mandokhel, said Salman's convoy and district police officer Lasbela Bashir Brohi were crossing the area when the huge explosion occurred.
No group immediately claimed responsibility for the attack in the insurgency-hit southwestern province.
According to a media report, however, the Baloch Liberation Army (BLA) claimed responsibility for the attack that was carried out in response to the military operation in various areas of Balochistan.