Turabi, the leader of the Shia party Islamic Tehreek Pakistan, was injured when the attacker detonated a bomb at the gate of his house as he was getting into a car.
The cleric later died in hospital, along with his cousin and a bodyguard.
Aftab Khan Sherpao, Pakistan's interior minister, condemned the blast and promised to find those responsible for organising the attack.
Sherpao said: "This is an act of terrorism, but at this stage we cannot say who was behind it."
Turabi had narrowly escaped an attempt on his life in April when a roadside bomb went off near his car.
Pakistan has been blighted for years by violence blamed on extremist elements among its Sunni and Shia sects.
Both sects have generally attacked places of worship and religious leaders.
In April, a suicide bombing at a Sunni gathering at a park in Karachi killed 57 people.