In one of the deadliest incidents, at least nine people died when a temple collapsed in the state's capital, Shimla.
Officials fear more people may still be trapped beneath the rubble.
Chief Minister Sukhvinder Singh Sukhu said heavy rains triggered landslides and flash floods in the hill state.
Hundreds of roads have been closed and parts of the Kalka-Shimla railway have washed away.
Mr Sukha posted on X about a flash flood and cloudburst - a sudden, very heavy fall of rain - that had occurred in other parts of the state, in which 14 people had died.
He also shared a video of the floodwaters in Mandi, where a torrent of water - that looks much like a river - can be seen moving downhill over main roads and houses. He described the video as "disturbing" and said seven people had been swept away by the water.
Thousands of tourists visit the hill state of Himachal Pradesh, especially its capital Shimla, around the year to enjoy its cool weather and picturesque scenery.
But the state has been experiencing heavy rains during the monsoon season, leading to flooding, landslides and cloudbursts which cause further damage.
Many factors contribute to flooding, but a warming atmosphere caused by climate change makes extreme rainfall more likely.
The world has already warmed by about 1.1C since the industrial era began and temperatures will keep rising unless governments around the world make steep cuts to emissions.
Videos shared on social media over the past few days show vehicles and buildings being swept away by gushing rivers, trees falling on cars and tourists stranded due to road closures.
Mr Sukhu has appealed to people to stay indoors and not go near rivers.
Incessant rains have also been battering the neighbouring state of Uttarakhand for the past couple of days, where officials fear several people have been buried in landslides.
The hill state is home to many revered Hindu shrines and sees a large number of tourists around the year.
On Monday, officials said that the Char Dham Yatra - a pilgrimage to the four holiest sites for Hindus in the state - has been suspended for two days due to the rains.