A third woman, aged in her 30s, was treated for minor injuries.
Video filmed by witnesses and posted on social media, showed a fight between several women in the street at the location of the incident.
During the incident, one woman got into a car which then moved forward and hit another woman, standing on the pavement.
A man standing nearby with a bike also appeared to have been hit by the vehicle.
Det Ch Insp Alison Foxwell has called for witnesses to come forward.
She said: “As our enquiries continue, our thoughts are with those injured and their loved ones.
“While this incident took place in the early hours of the morning, venues in the area were still open, and we believe a number of people will have seen what happened.
“I would urge anyone who witnessed the collision, or any activity prior to it that they feel may be of relevance, to come forward.
“The information you have – however minor you believe it may be – could be of crucial importance to investigators.”
