A woman who drove the wrong way around a roundabout led police on a chase through North Canberra before crashing her car and running away.

Police said the driver reached speeds of about 120km/h in a 60km/h zone as she tried to get away.

"About 12.20am police were patrolling along Majura Avenue in Dickson when they observed a silver Mitsubishi Lancer driving the wrong way on the roundabout at the intersection of Davenport Street," they said in a statement.

The driver sped away when police activated their lights and siren.

"The driver turned onto a number of suburban streets before running up a gutter onto the Downer oval, and into a low fence. The collision occurred around three minutes after the driver first fled from police," they said.

"Police were unable to locate the driver however, members of the public reported seeing a woman running from the scene down Melba Street shortly after the crash."

Police ask anyone who saw the incident to contact Crime Stoppers on 1800 333 000, or at www.act.crimestoppers.com.au.