Stephen Boyd, who is a suspect in the death of Tina Kontozis in her Bundeena home on Sunday, hit his head on the steering wheel when his car hit an embankment during a police chase on Monday, NSW Police said.

Mr Boyd was arrested, and taken from Queanbeyan Police Station to Queanbeyan Hospital on Monday night. He was transferred to Canberra Hospital on Tuesday morning for treatment of a broken jaw and neck injury.

He had surgery at Canberra Hospital and was expected to stay at least overnight. He remains under police guard while officers apply for an arrest warrant.

There will be a bedside hearing once he is recovered from surgery, police say.

NSW Police will likely then have to apply to the ACT Magistrates Court to have him extradited back to NSW, to face charges relating to Ms Kontozis' death.

The 51-year-old was the subject of a manhunt in NSW after the death of his former partner Tina Kontozis, who was reportedly bashed to death with a cricket bat in her Bundeena home on Sunday.

Police were called to the home in Beachcomber Avenue in Sydney's southern outskirts about 3.30pm after neighbours heard fighting and screaming.

Officers set up checkpoints and conducted an air search of bushland in the surrounding Royal National Park for Mr Boyd.

On Monday, highway patrol officers spotted Mr Boyd's car, a silver 2002 Holden Commodore sedan with NSW registration plates BZ 53 ZO, travelling along the Kings Highway at roughly 3.40pm.

Police followed the car and eventually stopped Mr Boyd on Wallace Street, Braidwood at 4.55pm on Monday.

He was treated by paramedics for minor facial injuries and was taken to Queanbeyan Police Station.

Detective Chief Inspector Terry O'Neill, the Sutherland Local Area Command Crime Manager, said Mr Boyd was known to police, but would not comment on whether there was a history of domestic violence in the case.

- with Kim Arlington and Kate Aubusson