A police spokeswoman said they signalled for a vehicle to stop on State Highway 1, Green Island, at about 2.30pm.
However, the vehicle failed to do so.
Police did not initiate a pursuit and instead followed the vehicle at road speed.
While attempting to flee police, the vehicle crashed down a bank, the spokeswoman said.
The sole occupant, a 16-year-old, was uninjured and taken into custody.
They would be referred to youth services.