The accused, identified as Amin Yusuf Khan, has been arrested, a police official said.
The incident took place at around 12.30 am in the Crawford Market area under Pydhonie Police Station limits when the man lost control over his high-end Mercedes, as a result of which it rammed into a pavement and hit five persons who were sleeping there, he said.
The five injured persons, identified as Munira Sheikh (25), Rahul Moinuddin Shaikh (4), Alisha Shaikh (40), Rashida Sheikh (20) and Ayesha Khatum (50), were immediately rushed to J J Hospital in South Mumbai.
Four of them were discharged this morning, while one of the victims, Munira, was shifted to GT Hospital where she was being treated for a fracture, police said, adding that her condition was said to be stable.
Khan has been arrested and booked under sections 279 (rash driving or riding on a public way), 337 (causing hurt by act endangering life or personal safety of others) and 338 (causing grievous hurt by act endangering life or personal safety of others) of the IPC, and relevant sections of the Motor Vehicle (MV) Act, police said.
He will be produced in a court on Friday, police said, adding that Khan was detained at around 1.30 am and formally arrested at around 4 am after spot punchanama was completed.
Further investigation in the case is on, police added.