The body of one jawan had been recovered, whereas five bodies were yet to be traced, Kinnaur Deputy Commissioner Gopal Chand said.
The avalanche occurred at around 11 am near Shipkala on the Sino-India border, he added.
Several jawans of the Indo-Tibetan Border Police (ITBP) were also trapped in the avalanche. However, they had been rescued, Chand said.
According to Army sources, 16 jawans had gone towards the Shipki La border post from Namagya in order to repair a damaged water supply line when the avalanche struck, burying six of them alive. One of them was rescued, but he succumbed to his injuries subsequently.
An Army spokesperson said the search-and-rescue operation would go on till the last man was retrieved.
A team of about 150 persons, including Army and ITBP personnel, is searching for the trapped jawans, along with the police.
Confirming the incident, Defence PRO Amit Gaur told PTI that the Army would issue an official statement on Thursday.