Witnesses said plain clothes policemen on Wednesday escorted Peter Hounam, who had been preparing a new documentary about Vanunu, to his Jerusalem hotel. They searched his room and then bundled him off in a car.
A spokesman from the prime minister's office, which oversees Israel's security services, confirmed the journalist had been arrested. A government gag order prevented release of further details in the case.
According to the website of the leading Yedioth Aharonoth newspaper, Hounam was being questioned on suspicion of committing "security offences".
Vanunu said the arrest was part of "the continued war by the Shin Bet internal security service against me and my supporters and those who want to raise Israeli nuclear secrets."
In 1986, Hounam secured an exclusive interview with Vanunu, a former technician at the Israeli atomic reactor in Dimona. His story in London's Sunday Times led independent analysts to conclude Israel had stockpiled as many as 400 nuclear weapons.
Israel abducted Vanunu and jailed him for 18 years. Hounam came to Israel to greet Vanunu when he was freed on 21 April and has since spent time with him in a Jerusalem church despite Shin Bet restrictions on Vanunu's contacts with the media.
Hounam was making a documentary on Vanunu for the BBC, which expressed grave concern over his arrest.
"We are aware that Peter Hounam has been arrested. We are very concerned at this development," a BBC spokeswoman said.