Rescue teams reached the scene but struggled in the dark and steep terrain, with the army later joining the search.
Six bodies had been recovered so far but there were fears for many more still missing, said Sandeep Kadam, a senior official at the scene.
"The other bus has been swept away, 800 metres down the steep hillside. We are not sure how many people were in this bus," he told AFP.
The Press Trust of India reported 30 people were feared dead in the disaster, while other reports suggested an even higher toll.
Some houses and slum dwellings were also destroyed in the landslide, which followed days of heavy rain in the Himalayan region.
Landslides are common in India, especially during monsoon months when heavy rain loosens steep hillsides.
At least five people were killed last month in a mudslide in remote Arunachal Pradesh state along the border with China.
Hundreds have died across India in torrential rain, floods and landslides since the onset of the wet season in April.