The tragedy happened at Murud beach in the Raigad district of Maharashtra state, said assistant inspector of police Arvind Patil.
“A total of 155 students from Pune went to Murud main beach and some of them went swimming around 3.30 pm this afternoon,” he told AFP.
“Thirteen students are dead due to drowning. The victims were all aged between 19 and 23,” Patil said, adding that 10 women and three men died.
“Local people and police are engaged in rescue operations,” he added, saying it was not yet clear whether all the students had been accounted for.
The victims were enrolled at Abeda Inamdar College, an arts, science and commerce institute in the city of Pune in Maharashtra. Media reports said they had gone to Murud for a picnic.
Murud sits on the Konkan coast, which has dozens of beaches popular with locals who prefer it to the internationally renowned tourist state of Goa.
Murud is around 140 kilometres (90 miles) south of Mumbai.
Monday’s drowning tragedy was the latest in India, where many people are unable to swim.
In February 2014, 29 people died when a passenger boat capsized in the eastern state of Orissa.
A month prior to that incident, 21 people were killed when a tourist boat capsized off India’s remote Andaman Islands.