The duo were proceeding to Perundurai when the rider lost control of he vehicle and it rammed the median wall on the road in Moolakarai, they said.
Under the impact, both fell off the bike and sustained serious bleeding injuries.
While the rider died on the spot, the other person was being treated at a private hospital, where his condition is reportedly critical, police said.
The identity of the students is yet to be ascertained, police added.