West Midlands Police said they believe a group of up to 15 men were involved in a violent dispute in the middle of the road on Bordesley Street when a light grey car was driven at them at around 11.25pm.
Two women who were not involved and were waiting to get a taxi on the corner of Bordesley Street and Trent Street were hit by the vehicle, which was then driven away at speed.
The women, both aged 20, received serious leg injuries and are recovering in hospital.
No one has yet been arrested but officers have been carrying out CCTV and other enquiries.
Officers are particularly keen to speak to anyone with footage of what happened, or those who might have dashcam footage from the area at the time.
Det Ch Insp Jim Mahon, of Birmingham Police, said: “This was an appalling attack where a car has been used as a weapon and two women who were not involved in any way have been seriously injured as a result.
“This was incredibly reckless and indiscriminate, and our investigations so far lead us to believe that what happened may have been caused by a dispute between two men.
“We also believe that another man who may have been injured left the scene. The car involved will have suffered damage to the front, so we are appealing for anyone with information on that vehicle, or the injured person who left the scene, to get in touch.”
Anyone with information should get in touch via 101, Live Chat on the West Midlands Police website or Crimestoppers on 0800 555 111 quoting incident number 20/100996/25.