The incident happened Wednesday night near a border outpost Naushera Dhalla in the Amritsar sector of the border with Pakistan, around 40 km from here.
A BSF spokesman said the intruder had crossed the border and was moving close to the barbed wire fence located inside Indian territory.
"He was challenged by the BSF but he continued with his aggressive posture. BSF troopers then fired at him. His body was recovered (Thursday) morning," the spokesman said.
India and Pakistan have a 553-km international boundary in Punjab. The BSF has seized over 245 kg of heroin along the border in Punjab this year.