Thirty-two pupils have been rescued so far and three bodies, said to be girls, have been found, according to reports.
Ships have been diverted to the area near Dahanu, in Maharashtra state, to help with the rescue.
The boat had been overcrowded and the pupils were not wearing lifejackets, the Times of India reported.
Two of those who died were reported to be aged 17.
The students were said to be from the KL Ponda High School in Dahanu.
NDTV reported that the accident may have happened because a number of students went to one side of the boat to take selfies, causing it to overturn.
Distraught relatives crowded on nearby Parnaka beach to wait for news.
Indian President Ram Kovind said his thoughts were with the families of those who had died.
Boats in India are often overloaded and lax safety standards mean accidents are common.
In November at least 16 people drowned when their boat capsized in the southern state of Andhra Pradesh.
In a separate and unrelated incident, the bodies of four people have now been found after a helicopter crashed into the sea off Mumbai.
The Pawan Hans helicopter had been carrying five senior employees of Indian oil exploration firm ONGC and two pilots when it went missing 15 minutes after taking off from Juhu.
The coast guard said the wreckage had been found and the search for those still missing was continuing. It is not known what caused the accident.
Two of the dead, both ONGC employees, have been identified by ID cards.