The victim, Shubhankar Chakraborty (27), hailed from Palta in North 24 Parganas district of West Bengal, they said.
No suicide note was found from his house in east Delhi's Shahdara where he was found hanging from a hook in the ceiling with a plastic wire around his neck, the police said.
However, before taking his life, Chakraborty updated the cover photo of his purported Facebook profile that said "I quit".
He had a fight with his father who visited him two days ago and it is being probed if he took the extreme step due to the fight. No one has raised any suspicion on the death, the police said.
The Facebook live stream purportedly showed him climbing atop a cooler, wearing Delhi Metro's uniform. He looked into the camera a couple of times and kissed his company identity card twice before taking his life.
A mobile phone kept buzzing in the background as he allegedly hung himself.
"He had joined the Delhi Metro Rail Corporation in June and was a staffer in the Electrical and Maintenance Department," a source said.
Suryakant Das, a friend of Chakraborty, informed Farsh Bazar police station around 9.05 am about the incident, according to the police.
In his statement to the police, Das said his friend Akash informed him around 8 am that he had seen a live video of Shubhankar, in which he was seen hanging himself from the ceiling fan hook of the room.
Das then informed about it to his other friend Rajender Ojha, and when they reached his house, the room was found to be shut from inside. Then Das peeped into the room through a window and he noticed that Shubhankar was hanging from the ceiling, the statement said.
The family has been informed and the body has been shifted to Subzi Mandi mortuary, the police said.
He has a sister who is married. His wife lives in West Bengal and his mother died 16 years back, they added.