The driver of the car fled from the spot after hitting the rickshaw with the victims in it around 12:43 AM, a senior police official said.
Police said that they have got clues about the vehicle.
"The PCR call that was made said that the offending vehicle is a white-coloured Audi. However, from the CCTV footage that we have procured it has been found that it might be a white-coloured Skoda. However, we have sent the footage for forensic examination in order to get a clear picture," the official said, adding a hunt is for the accused.
Singh and three of the injured work at The Masala Factory restaurant in Tagore Garden and hail from Uttarakhand.
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The rickshaw puller is yet to be identified since he is not fit for statement and is currently undergoing treatment at the Safdarjung Hospital, the official said.
Eyewitnesses told police that it was a head on collision between the car and the rickshaw. The rickshaw was coming from the wrong direction when the car hit it near the metro station.
The injured were rushed to nearby Kukreja hospital where Ram Singh was declared brought dead, while his brother Rahul Singh (20), Dilip and Anand Prasad (24) are undergoing treatment.
Police is tracing the route taken by the car after hitting the rickshaw.