"Alert troops of the army noticed suspicious movement on the LoC in Krishna Ghati sector around 2.30 am," Defence Ministry spokeman, Lieutenant Colonel, Manish Mehta told news agency IANS.
The body of the intruder has been recovered, said army officials.
Meanwhile, an army porter was killed while another sustained injuries in a ceasefire violation by Pakistani troops along the Line of Control in Keran sector of Kashmir.
"Pakistani troops violated the ceasefire along the LoC in Keran sector yesterday by resorting to unprovoked firing, resulting in death of one army porter and injuries to another," an army official told Press Trust of India.
The body of the killed porter was retrieved and handed over to his family for last rites while the injured was evacuated to a medical facility, the official said.
Curfew has been imposed in large parts of Srinagar and some other districts of Kashmir Valley after protests and clashes following the killing of Hizbul Mujahideen commander Sabzar Ahmad Bhat on Saturday. Bhat, who has succeeded Burhan Wani, is among the 10 terrorists killed by the security forces in separate encounters in the last 48 hours.
The separatist groups have called for a two-day strike.
One civilian was also killed in security forces firing in south Kashmir's Tral on Saturday as protests broke out in the Valley following the death of Bhat.
Mobile internet services that were briefly restored on Saturday morning were snapped again. Shops, schools and colleges in many parts of the state closed down.
Violent protests had broken out in Kashmir last year in July after Burhan Wani was killed, leaving more than 100 people dead and over 12,000 injured.
(With inputs from IANS)