Three others were wounded in the rocket fire and are in light condition.
Qassem is a veteran figure in the group, having served as Deputy Secretary-General for the Lebanon-based terrorist organization for over three decades.
This step has been previously avoided due to legal challenges and possible international ramifications.
Georges Ibrahim Abdallah, a Lebanese terrorist, has served 40 years for the killing of two diplomats.
The massive rise in lawlessness in the Negev has also fueled the rise in terror attacks.
A woman in her 50s sustained serious wounds, and two aged 21 and 13, respectively, sustained light wounds from smoke inhalation.
The driver has been apprehended and emergency services are at the scene treating the wounded.