Kakar, a lawmaker belonging to Balochistan Awami Party (BAP), will lead a caretaker government until a new election later this year.
Senior police officer Aizaz Ghoraya confirmed that security and intelligence officials recovered Shahbaz from the Kuchlak area on the outskirts of Quetta city.
No group claimed responsibility for the attack but the Taliban usually target shrines as they consider it un-Islamic.
The blast was claimed by both the local affiliate of the Islamic State terror group and by Jamaat-ul-Ahrar, a splinter group of the Tehrik-e-Taliban Pakistan.