Emergency services were called to Hennef Way after the crash involving a black car at around 10pm on Saturday, February 16.
The 30-year-old woman was taken to the John Radcliffe Hospital with a back injury where she remains, a police spokesman said.
The man, 32, was arrested on suspicion of driving a motor vehicle dangerously and driving a vehicle involved in a road accident and failing to report that accident before being released under investigation.
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Anybody who witnessed the collision, or who may have dash-cam footage, is asked to call 101, quoting reference number 43190050964.