The deceased have been identified as Ashok (30), his wife Kiran, his son Ishant and one Jawahar Singh (93), all residents of Najafgarh area, they said.
Police said that the incident took place around 5.15 am when the deceased persons were out on a morning walk.
"Ashok's another son Dev is in a serious condition and admitted in a hospital. The driver, identified as Rajesh (35), was apprehended at the spot," Deputy Commissioner of Police (Dwarka) Santosh Kumar Meena said.
Police said that the tempo was being driven very rashly and in a negligent manner.
The driver's medical is being conducted and a case under section 279 (rash driving or riding on a public way) and 304 (punishment for culpable homicide not amounting to murder) of the Indian Penal Code (IPC) has been registered, they said.
The bodies have been sent to the Rao Tularam Memorial Hospital for post-mortem and an investigation is underway, police said.
Further details are awaited.