Army radio said he was arrested in the morning after an interview on privately owned Channel 2 last week in defiance of the terms of his 2004 release following an 18-year jail term.
He later appeared in a Jerusalem court and was confined to his home for a week and barred from using the Internet, the radio said. Court officials could not be reached for confirmation.
The former nuclear technician was jailed in 1986 for disclosing the inner workings of Israel's Dimona nuclear plant to Britain's Sunday Times newspaper.
He spent more than 10 years of his sentence in solitary confinement.
In Friday's interview, the content of which Channel 2 said was cleared for broadcast by the military censor, he said he longer has any secrets to spill and just wants to join his new bride in Norway.
"I got married three months ago to my wife who is in Norway," he said. "She is the wage-earner; she is the one who is working. She can't live here. I want to start living my life."
Vanunu married Norwegian theology professor Kristin Joachimsen at a Lutheran church in Jerusalem on May 19.
The sixty-year-old converted to Christianity shortly before being snatched by Mossad agents in Rome and smuggled to Israel.
Released in 2004, he was jailed again for 11 weeks in 2010 for breaking theterms of his release by meeting a foreigner, a prison official said.
In 2011, the High Court barred him from emigrating on the grounds that he still poses a threat to state security.
He is barred from speaking to journalists but has repeatedly given interviews to foreign media, while shunning the Israeli press until the Channel 2 appearance.
Israel is the Middle East's sole if undeclared nuclear power, refusing to confirm or deny that it has such weapons. It has refused to sign the nuclear Non-Proliferation Treaty or to allow international surveillance of the Dimona plant in the Negev desert of southern Israel.