The militant, who had taken three persons hostage in a school in a village near the area, was arrested after an operation was launched by the army and the police, Deputy Commission, Udhampur, Shahid Iqbal Chaudhary said.
All the hostages have been freed and the operation has ended, he said.
The militant strike was the first in Udhampur district in over a decade coming days after terrorists attacked Dinanagar Police Station in Gurdaspur in Punjab.
Two BSF jawans were killed and 13 personnel were injured, IG, BSF (Jammu Frontier), Rakesh Kumar said.
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The militants hurled grenades and opened indiscriminate fire on the convoy when it reached Nassu belt on its way from Jammu to Srinagar, IG Jammu, Danish Rana said, adding that the BSF jawans retaliated, killing one of the two militants.
The injured jawans have been taken to a hospital, he said, adding a massive combing operations has been launched by the army and the police in and around the area which has been cordoned off. Vehicular movement on the highway has been stopped due to the incident.
The government and the security forces were doing their best to tackle such evil designs and "without a doubt the country's respect, honour and the people's security is the government's topmost priority," he said in Delhi.
Congress leader Ambika Soni said, "Ever since the new government has come in, there have been attacks happening every day. It is impossible for people to live on the border along Rajouri, Poonch and other areas that touch Pakistan."