"Everyone is just trying to punch taxi drivers, or Indian people. Why? We don't have any problem. If you can't afford a taxi or if you can't afford any cab just [get] out, don't come in."
He told the Herald the situation first escalated when the woman asked him to allow two more of her friends into the vehicle on Victoria St, which would have been over the legal limit as there were already three passengers in the car.
Singh said she urged him to take the extra passengers, reassuring him that there were "no police" around.
"I said no, I can't break the rules. She said 'I can give you $10, $20', I said it's not about that."
When he refused, Singh said the racist abuse, yelling and punching began.
Police told the Herald they received a report of an assault that took place inside a vehicle on Victoria St about 3am on Thursday.
A spokesperson said one person received a cut to their face during the incident.
"Police have spoken with the victim and are making follow-up inquiries."
Singh said the whole situation was recorded on his in-car camera and a security guard witnessed the attack.
After the incident, Singh said the woman ran away but he had her address from a previous trip she had taken and has given this to police.