The disaster, which authorities said had affected some 22,000 people, was the latest in a series of deadly weather events in South Asia's mountains blamed on climate change.
"The search operations are being undertaken under conditions of incessant rains, fast-flowing water in Teesta River, roads and bridges washed away at many places," a defence spokesperson said on the social media platform X, formerly Twitter.
A cloudburst dropped heavy rain in a short period on the Lhonak glacial lake on Wednesday, triggering flash floods down the Teesta Valley, about 150km north of Gangtok, capital of Sikkim state, near the border with China.
The state disaster management agency said 26 people were injured and 102 were missing as of early Thursday.
Eleven bridges were washed away.
Video footage from the ANI news agency showed floodwaters surging into built-up areas where several houses collapsed, army bases and other facilities were damaged and vehicles submerged.
The weather department has warned of landslides and flight disruptions, with more rain expected in the next two days in parts of Sikkim and neighbouring states.
Other mountainous areas of India and parts of neighbouring Pakistan and Nepal have been hit by torrential rains, flooding and landslides in recent months, killing scores of people.
Last year, Pakistan blamed climate change for unprecedented floods caused by historic monsoon rains that washed away roads, crops, infrastructure and bridges and killed at least a thousand people.
"Sadly, this is the latest in a series of deadly flash floods that ricocheted across the Hindu Kush-Himalayan region this monsoon, bringing the reality of this region's extreme vulnerability to climate change all too vividly alive," said Pema Gyamtsho, director general of the Nepal-based International Centre for Integrated Mountain Development.