The incident took place at Mandari, about 50 km from here, when the driver lost control over the car while negotiating a sharp turn and it fell into the 200-feet-deep gorge, they said.
The victims were returning to Shavali village from Dhami, police said.
While the six people, including a child, died on the spot, the two injured were rushed to Indira Gandhi Medical College hospital here.
The Himachal Pradesh government has announced an immediate relief of Rs 10,000 to the next of kin of the dead and Rs 5,000 to the injured. PTI PCL