A woman has been airlifted to hospital in a critical condition after an alleged domestic violence incident in southwest Sydney.

The 36-year-old allegedly had a glass smashed over her head at a home on Maddison Crt, Narellan Vale, and called triple-0 about 8.30am on Wednesday.

While waiting for emergency services to arrive outside the home, police believe she was run over by a vehicle which then fled the scene.

Paramedics treated the woman before airlifting her to Liverpool Hospital with critical injuries, including a broken pelvis, internal injuries and cuts to her head.

Police arrested a 36-year-old man, alleged to be her partner, at a phone box in Camden Valley Way about 11am. He was taken to Narellan Police Station where he is assisting police with inquiries.

Detective chief inspector Paul Albury said police arrived to find a “horrendous scene” and located three unharmed children, aged between six and 12, at the home.

He said police expect to bring charges against the man currently in custody, alleging the incident was sparked by an argument shortly prior.

“That argument continued inside the premises … The man (allegedly) struck the woman with a glass,” Albury said.

He noted police engaged a number of resources during a “frantic” search for the man which also located the vehicle he allegedly fled in.

Investigators have established a second crime scene where the vehicle was found.

Albury confirmed police had been called to the home before, but never for a domestic violence incident and there are currently no AVOs out for the couple.

While charges are yet to be laid, Albury said domestic violence-related incidents are “our most frequent crime”.

“Here in Camden, we attend one every two hours,” he said.

“It’s imperative that we as a community take up the fight together. If you see something say something.”

Police have urged anyone with information, including CCTV footage and dashcam footage, to contact Crime Stoppers.