The man shot himself in the head in the intervening night of Sunday and Monday, the officer said.
The incident took place at Saichak under the jurisdiction of Beur police station where 19-year-old Akash Kumar took out a gun and pulled the trigger at himself while chatting with the girl via Whatsapp video call, Deputy Superintendent of Police (DSP) Ramakant Prasad told PTI.
He said the matter came to light when police reached the man's house to investigate the suicide, seized his mobile phone and examined its call history.
He got agitated at the end of the prolonged video chat, picked up a gun and shot himself in the head. He died on the spot, Prasad added.
"We have seized the girl's mobile phone too. Further investigations are on. If a written complaint is received from either side, a case of abetment of suicide would be lodged", he added.