The theft of the Audi A3 convertible car happened in Iveson Drive, West Park, after the victim had parked it to make a phone call at around 7.15pm on Monday.
A man then opened the driver's door and demanded the keys.
The 35-year-old refused, and was hit in the face with a large piece of stone and punched several times as she struggled with the robber.
She was eventually pulled from the vehicle and the suspect drove off.
Police said that a short time later, the car was involved in a collision with another vehicle in Butcher Hill but drove off and was found abandoned on Lea Farm Mount, Hawksworth.
PC Darren Machell, of the Leeds District Crime Team, said: "This was a terrifying experience for the victim in what was a vicious and sustained attack by the suspect. She suffered serious injuries as a result of the attack, including a broken nose, and she is understandably shaken and upset by this incident.
"The suspect has used extreme violence to commit this offence and it is vital the we identify him at the earliest opportunity.
"We would urge anyone who witnessed the incident or who has any information that could assist the investigation to contact us immediately."
Anyone with information is asked to contact PC872 Machell at Elland Road via 101 quoting crime number 13160710654 or call the independent charity Crimestoppers anonymously on 0800 555 111.
Two men, aged 14 and 18, and a 30-year-old woman have been arrested in connection with the incident and are currently on bail pending further enquiries.