According to German media reports, the 44-year-old was shot by someone in a passing car, while she was in another car. A wide-ranging search is underway to track down the perpetrator.
According to initial findings, the woman was on Frankfurter Straße (near the Luisenstraße junction) shortly before 7pm on Thursday evening when the incident happened.
Bild reported that police spokesman Henry Faltin said: “She was sitting in her car when the car drove by.”
Shots were fired at the car the woman was in. The woman died at the scene, while the car from which she was shot at raced away.
The perpetrator is thought to have been in a grey Audi. The Audi is said to be a rental car.
A large-scale search was launched after the alarm was raised on Thursday. Officers were able to find and secure the Audi in Klingsporstraße but the shooter is still at large.
The public prosecutor's office in Darmstadt has taken over the investigation. No more details have been released at this stage.
An autopsy is being conducted on Friday morning, after which Bild reports that the police and prosecutors are set to release more information.