The students were on a leisure cruise off islets around Jaffna when their boat capsized, police said in a statement.
The victims, aged 19 and 20, were celebrating a birthday when the accident occurred. Only one passenger made if off the craft unscathed.
Navy divers were searching for the missing student, while the bodies of the others have been taken to Jaffna hospital, 400 kilometres north of the capital Colombo.
Many overcrowded boats capsized in the north during the war, leading to countless casualties, as Tamils tried to flee fierce fighting in Jaffna.
Much of Jaffna, the cultural capital of Sri Lanka's minority Tamil community, was destroyed during the war, but large parts have been rebuilt.