Rescuers were digging through debris searching for residents after overnight landslides struck homes built on slopes in the towns of Mirik, Kalimpong and Darjeeling in West Bengal state.
"At least 11 bodies were dug out of debris of landslides in Mirik, Kalimpong and in the town of Darjeeling. More than 20 people are injured," said West Bengal police inspector-general Anuj Sharma.
"The landslides have also brought down a number of homes on the slopes of the hills," he told AFP from the state capital Kolkata.
"We fear that many people are buried under debris."
Read:Heavy Downpour: School damaged by landslide
The Press Trust of India news agency said 18 people were killed in the picturesque hilly area, adding that numerous landslides have also cut roads and telephone links.
Another officer described mud and water cascading down hills in Mirik, a small tourist town, and Kalimpong hill station further north.
"The rush of mud and water tore down everything in its path in Mirik and Kalimpong," police superintendent of Darjeeling district, Amit P Javalgi, told AFP.
"It's still raining in the hills of Darjeeling. Rescue work is on," he said.
Darjeeling district, a tourist attraction known for its lush green tea plantations, is some 600 kilometres (372 miles) north of Kolkata.
Floods and landslides hit South Asia every year during the monsoon season.
Further west in the state of Gujarat, floods caused by the annual rains last week left at least 55 people dead.
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