The unsourced ABC story named the man, known previously only as "prisoner x", as Ben Zygier. It added that it "understood" the 34-year-old from Melbourne had been previously recruited by the Israeli spy agency Mossad.
There was no official comment on the story in Israel.
However, within hours of the report surfacing, Prime Minister Benjamin Netanyahu's office summoned Israeli editors to ask them not to publish a story "that is very embarrassing to a certain government agency", Israel's Haaretz newspaper said.
"The emergency meeting was called following a broadcast outside Israel regarding the incident in question," Haaretz said, giving no further information.
Shortly afterwards, all reference to the Australian report vanished from Israeli news sites - including Haaretz itself.
Such a gag order is highly unusual in Israel, where state military censors normally allow local media to quote foreign sources on controversial incidents - such as an alleged attack on Syria last month by the Israeli airforce.
ABC said that Zygier's imprisonment was so secret that not even his guards knew his name. However, word got out at the time of a mysterious prisoner and human rights groups wrote to the state to demand more information.
"It is insupportable that, in a democratic country, authorities can arrest people in complete secrecy and disappear them from public view without the public even knowing such an arrest took place," the Association for Civil Rights in Israel wrote in June 2010.
When Israel's Ynet website wrote about the case that same month the story was quickly removed because of a gag order.
ABC said Zygier had moved to Israel 10 years before his death and changed his name to Ben Alon. It gave no reason for his imprisonment, speculating only that it would have had to concern espionage and sensitive state secrets.
Funeral notices from Australia show that Zygier's body was flown back to Melbourne at the end of December 2010 for burial.
© Thomson Reuters 2013