The police said the army personnel, identified as Rifle man Bhupal Mukhia, was arrested by the anti-hijacking squad from Srinagar's civil airport.
He has been taken to for interrogation in central Kashmir's Humama. Mukhia told the police he was carrying the grenades so he could cause a blast in the river from which he wanted to catch fish.
Mukhia is a resident of village Bhosoli Gaom in Darjeeling.
More details are awaited