The statement said the “unidentified terrorists” took “advantage of heavy rains and low visibility in the area.”
“The vehicle caught fire due to likely use of grenades by terrorists,” it added.
There was no independent confirmation of the incident.
Nuclear-armed rivals India and Pakistan each administer part of Kashmir, but both claim the territory in its entirety.
Rebel groups have been fighting since 1989 for Kashmir’s independence or merger with neighboring Pakistan.
Most Muslim Kashmiris support the rebel goal of uniting the territory, either under Pakistani rule or as an independent country.
New Delhi insists the Kashmir militancy is Pakistan-sponsored terrorism. Pakistan denies the charge, and most Kashmiris consider it a legitimate freedom struggle.
Tens of thousands of civilians, rebels and government forces have been killed in the conflict.