Mr Sukhu urged everyone to vacate their houses if they notice any cracks.
At least four houses perched on a hillside in Shimla have been washed away by a landslide caused by heavy rain, which has been battering parts of Himachal Pradesh since last week. Two people have died and 5-10 are feared trapped.
The incident took place in the city's Krishna Nagar area around 5.30 pm today. A disturbing video of the landslide shows a tree leaning precariously and then falling on one of the houses, whose roof gets damaged. There's a heart-stopping pause for a few seconds until the ground gives way, sending the damaged house and at least three others crashing down the hill.
Himachal Pradesh Chief Minister Sukhvinder Singh Sukhu said two people died in the incident.
"Two people have died. We have recovered one body and we can see the leg of another. That body is also being pulled out. About 35 people had been evacuated from their houses. I would urge everyone to vacate their houses if they notice any cracks. The administration will ensure food and lodging for them, and we will also give money to rebuild damaged houses," Mr Sukhu said.
Officials said 5-10 people are feared trapped in the debris and rescue operations are underway.
Himachal Pradesh Additional Director General of Police (Law and Order) Abhishek Trivedi said several people had already vacated the houses after they noticed cracks. "But we suspect around 5-10 people may be trapped. Teams of ITBP, SDRF and district police are at the spot. A rescue operation is underway," he was quoted as saying by news agency ANI.
The chief minister said 60 people have lost their lives in Himachal Pradesh since heavy rainfall began last week.
"We have held a meeting this evening. All educational institutes will stay shut tomorrow. We also discussed structural norms and drainage for roads. There has been a lot of damage because of the rain. Restoration will take time, but it will be done on a war footing," Mr Sukhu said.
Earlier in the day, the chief minister had said Union Home Minister Amit Shah had assured him of all help and that an Army helicopter has been deployed in Shimla.
An account of the Indian military posted on X, formerly known as Twitter, that the Western Air Command of the Indian Air Force had rescued over 150 people from affected areas in the state today.
The Indian Meteorological Department has predicted isolated heavy rainfall over Himachal Pradesh for the next two days and over Uttarakhand and northeast India for the next four to five days.
The heavy rain in Himachal Pradesh and Uttarakhand is the result of a fresh spell of western disturbance. "The location of the Monsoon trough lies along the foothills of the Himalayas and hence the South-westerly Arabian Sea monsoonal winds are hitting the Himalayan foothills," said the weather office.