Colonel Gurung of 27 Mountain Division stationed in North Sikkim told reporters that the fighter jet crashed at 1:15 pm.
The aircraft had taken off from Bagdogra airport near Siliguri in West Bengal, Col Gurung said.
According to eyewitnesses, Flight Lieutenant Yogesh Yadav, who was flying the aircraft, had bailed out.
Army troops have launched a search for him and his fate was not immediately known, Army sources said.
Rescue helicopter from Bagdogra has left for the spot.
According to eyewitness accounts, there was a loud bang before the plane crashed and the pilot ejected from the aircraft.