It took bomb disposal experts 10 hours to free the girl from the "very elaborate, sophisticated" device, the Australian Associated Press (AAP) quoted Assistant Commissioner Mark Murdoch as saying.
Two police negotiators had stayed with her throughout the "very, very difficult" ordeal, he said, but she had not been allowed to speak to her parents for operational reasons.
She had done "a great job keeping her emotions in check", the Sydney Morning Herald (SMH) quoted him as saying.
Reports said that police sought advice from British military experts, nearby properties were evacuated and streets cordoned off during the operation.
"The family have endured something no one needs to endure... but they have held up remarkably well," Murdoch said.
Afterwards Pulver was taken to hospital and examined by doctors, leaving on Thursday morning, AAP said, adding that police had now established the device did not contain any explosives.
Murdoch declined to say if the incident had been an extortion attempt, but said: "We haven't made any contact with who's responsible but hopefully that doesn't remain the position too much longer. We want to get our hands on who has done this.
"Certainly the family are at a loss to explain this, but you wouldn't expect someone would go to this much trouble if there wasn't a motive behind it."
The SMH said a balaclava-clad man had entered the house and placed the device on the girl. Other reports said a ransom note was attached to her neck and it was a case of extortion.
Her father was named by several media as William Pulver, a successful businessman who is chief executive of Appen Butler Hill, a linguistic solutions software company.
Investigations were being headed by the robbery and serious crimes squad, which also deals with extortion attempts.
Mosman is a wealthy suburb on Sydney's lower north shore lined with million-dollar homes.
The street where the incident happened is reportedly home to leading racehorse trainer Gai Waterhouse and ex-Australian rugby stars Phil Kearns and John Eales.