The sister of a Sydney teenager suspected of shooting himself in a game of Russian roulette read about it on social media before police could inform the family.

Josh Taylor, 19, remains in a critical but stable condition in Westmead Hospital after suffering a single bullet wound to the side of his head in the northwest suburb of Pitt Town on Friday afternoon, the Sydney Morning Herald reports.

Three friends who were with Mr Taylor at the time told police he took the gun, held it to his head and pulled the trigger, discharging the only bullet in the chamber just centimetres above his ear.

Word of the incident quickly spread to Facebook for Mr Taylor's sister to see.

It was then she reportedly phoned her mother to deliver the news before police even had a chance to contact them.

"I've (since) been in contact with his mother. She is obviously beside herself. We all just express our feelings for the family," Detective Inspector Garry Sims told the newspaper, urging people to be mindful about what they posted on social media.

The family is keeping vigil at Mr Taylor's bedside.

He is believed to be on a ventilator although how he survived being shot in the head remains unclear.

On Sunday afternoon, Mr Taylor's mother made an impassioned plea on Facebook for her son's recovery.

"Come on mate, fight!!! WE need you home with us … no words can comprehend," she wrote.

A handgun recovered from Mr Taylor's vehicle is being forensically examined and police are making inquiries into its origin.

Investigations into the shooting are continuing.