The mishap took place at around 1 AM when the labourers, who were working on a project under the Pradhan Mantri Gram Sadak Yojana, were asleep in their huts in Teoni-Hanol area when strong winds and thundershowers triggered a landslide, District Magistrate Ravinath Raman said.
The bodies of the 10 labourers have been retrieved and the injured admitted to a hospital, he said.
He said one of the injured, who is in "serious condition", is being taken to Dehradun for better treatment.
Rawat's media advisor Surendra Kumar said the Chief Minister has announced a compensation of Rs 4 lakh each to the next of the kin of the deceased.
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The deceased belong to three families from as many different districts in Nepal.
Members of one deceased family have been identified as Deepak, his wife Devi, and their children - Sanjana, Tara and Bharat Bahadur - from Salyan district in Nepal.
The other deceased family members have been identified as Vinita and her sons - Ravindra and Jeevan - from Jajarkot district in that country.