Jitender Singh lost control of his vehicle near Simthan last evening while on the return leg of the Mughal road rally, they said.
While Singh died on the spot, his navigator Ashish Mahajan was critically injured and has been admitted to a hospital.
The condition of Mahajan has shown no signs of improvement since last night, doctors attending on him said.
The third Mughal Road Car Rally began here on Saturday with 93 teams including Kashmir's first motorsport team, Baba Reshi Lions. It is scheduled to be flagged in later in the day.
The 600-kilometre long rally passes through the historic Mughal road that was once traversed by the caravans of Mughal emperors to reach Kashmir.