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.
The banned Baloch Liberation Army (BLA) has claimed responsibility for the attack.
Meerak Baluch, a spokesman of the group, called up media offices and claimed responsibility for the attack.
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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.
"The rickshaw driver, a 12-year-old child in the rickshaw and a passerby died at the spot," police official Ghulam Mustafa Shah was quoted as saying by Geo TV.
Seven policemen and eight others were also injured in the explosion. The vehicle in which the policemen were travelling was partially damaged.
"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.
According to television channels, the blast was so loud it was heard in nearby areas and glass windows of nearby shops were shattered as panic spread among local residents.