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The accident occurred at Pulghrat in Mandi district, some 132km from state capital Shimla, around 2.30pm IST.
"The pick-up vehicle carrying some 10 labourers from the eastern state of Bihar, was travelling towards Sundernagar from Mandi when the driver suddenly lost control of it while negotiating a bend, leading to the fatal accident," a senior police official told the media.
Local people retrieved six bodies from the Suketi rivulet in a search operation that lasted over two hours. "Two injured labourers were also rescued from the rivulet and rushed to a nearby hospital, where one succumbed to his injuries later in the day," the official said.
Indian Prime Minister Narendra Modi has expressed grief over the loss of lives. "The government is carrying out rescue and relief work," he tweeted, wishing the injured a quick recovery.
Police said a case has been registered against the driver of the vehicle for rash and negligent driving. "He had escaped unhurt, but fled from the spot. Efforts are on to nab him," the official said.
Road accidents are very common in India, with one taking place every four minutes. These accidents are often blamed on poor roads, rash driving and scant regard for traffic laws.
Indian government's implementation of stricter traffic laws in recent years have failed to rein in accidents, which claimed over 100,000 lives every year.