The incident took place in Sibi district when the NATO vehicle was travelling from Karachi to Afghanistan via the Chaman border crossing.
Police said the motorcycle-borne men fired at the truck, killing the driver instantly. "The cleaner who was with the driver later died in hospital," a police official said.
The attackers also set the truck on fire, officials said.
Since the Pakistan Tehrik-e-Insaaf stopped NATO containers from travelling through Khyber-Pakhtunkhawa province in the northwest, most supply trucks have been using the route via the troubled Balochistan province.