The students had stopped to take photographs on the edge of the Beas river in Himachal Pradesh when water released from a dam washed them downstream, transport minister G.S Bali said.
Rescue workers using torches in the dark were attempting to find the students in the picturesque Kullu Valley, some 200 kilometres (130 miles) north of the state capital Shimla, the minister said.
"Rescue teams are looking downstream for the missing in the dark," he said.
"They are 24 engineering students of the VNR college in Hyderabad," he said.
"The students had got off the bus to take photographs at the edge of the river at around 7:30pm when the sudden rise of water washed them away," he said.
The national government confirmed at least some of the students had drowned, with a rescue team sent to help search for survivors.
"I am deeply pained over the tragic incident of engineering students getting drowned in a flash flood in Himachal Pradesh," Home Minister Rajnath Singh said on his official Twitter account.
"I have instructed the authorities to despatch a rescue team for immediate action and save precious lives trapped in the floods," he said in a tweet.
A local official blamed the surge of water on a hydroelectric power plant further upstream.
"The water was released by the Larji power project dam," said senior state official Rakesh Kanwar said.
Angry locals and tourists blocked the main highway near the river in protest over the incident, saying authorities had failed to issue a warning about the release of water from the dam, according to local media.
The students, from the VNR Vignana Jyothi Institute of Engineering and Technology in the southern city of Hyderabad, had been travelling to the resort town of Manali further north.
The stunning Kullu Valley is home to raging rivers, dense forests and steep gorges.
Himachal Pradesh and other Himalayan states including neighbouring Uttarakhand are home to a string of hydroelectric projects as India rushes to expand power generation to meet rising demand.
Governments are attempting to harness the power of rivers despite the risk of environmental damage to diversify away from costly and polluting coal and gas plants to meet the country's electricity shortage.
A government report in April concluded that hydropower projects in northern India were partly to blame for devastating floods last year that killed thousands.