The vehicle in which the men were travelling was blown apart when it ran over the landmine late on Saturday in Pulwama, south of the summer capital Srinagar.
The powerful blast in Wachi village hurled the car skyward and left a 10ft-wide crater in the road, police officer Imtiyaz Ahmad said from the site of the blast.
"The car is completely damaged, totally twisted," he said.
"It was hurled several metres from the crater. The bodies of the victims are in pieces. It is a very awful sight."
A man claiming to be a spokesman for the Hizb-ul Mujahidin group said it carried out the blast in a call to a local news agency, the Central News Service.
Hizb-ul Mujahidin is the largest among the armed groups fighting Indian security forces since 1989 to carve out a separate homeland or merge Kashmir with India's neighbour, Pakistan.
The vehicle, a private 4WD that was being used by the army, was on night patrol when the explosion occurred, Ahmad said. The occupants included a major, eight army soldiers, a police officer and the driver of the vehicle, he said.
Five policemen and two separatists died in a gun battle on Saturday after the fighters entered a police camp in Sopore in northern Kashmir.
Clashes have increased in Kashmir in recent weeks. Some experts say the escalation could be aimed at derailing a new round of talks between India and Pakistan over the Himalayan region.
The two sides are due to meet later this week to consider a popular demand to start bus services between the two parts of Kashmir they control.
Nearly 45,000 people have died since the revolt against Indian rule began in Muslim-majority Kashmir in 1989 according to official figures. Separatists put the figure twice as high.