He told Al Jazeera that three of his bodyguards were killed. One civilian was also reported killed and three policemen were injured.
Other reports have quoted Dastageer as saying that the attacker first threw a hand grenade on the road in front of the convoy, slowing it down, and then jumped on one of the cars and detonated the explosives.
It is the second assassination attempt on Dastageer in nine months. An attack on November 18, 2007, killed his son and six of his bodyguards.
Nimruz province has been suspected of being a Taliban safehaven.
However, attacks in the west of Afghanistan are low compared to the south where Nato forces are stationed.