A police officer was injured in the arrest of the 28-year-old, who police say was breaching his bail conditions.

Police said the owner of the car - a silver Mazda RX8 - left the vehicle running in his Dunlop driveway about 9.20am to get something from inside.

On his return, the car was gone.

Shortly after, a woman walking her dogs on Wambo Place in Palmerston had to rush onto the footpath to avoid getting hit by the same Mazda fishtailing down the street.

The woman told police the car sped past a small child riding a bike.

Police said the car pulled up outside a house on Wambo Place around 10am. When the driver left again in the same car, residents saw him attempt a burnout, losing control and fishtailing down the road.

Around midday, an off-duty policeman reported a man acting suspiciously outside the Gungahlin Leisure Centre.

When police arrived, the man attempted to flee on foot but was arrested after a short chase. The man and a police officer were injured during the arrest.

The man was treated by ambulance paramdics then taken to The Canberra Hospital for further treatment.

He will be charged with two counts of breach of bail, taking a motor vehicle without consent, common assault, and reckless or dangerous driving.

Anyone who may have seen a silver Mazda RX8 driving yesterday is urged to contact Crime Stoppers on 1800 333 000 or via act.crimestoppers.com.au. Information can be provided anonymously.