"He has refused to give us his place of residence (after his release) and until he does so he will not be freed," a Prisons Authority spokesman said.
Vanunu, 49, was due to be released in the southern coastal city of Ashkelon at 11.00 am (08:00 GMT) on Wednesday after serving his full prison term for revealing Israel's nuclear secrets to a British newspaper.
Procedures to free him were underway when Vanunu, a former nuclear technician, refused to give authorities his place of residence as a condition of release.
Media reports say Vanunu will live in the luxury apartment complex of Andromeda Hill in the Jaffa neighbourhood in Tel Aviv where he will be under close supervision by security services.
Vanunu is banned from leaving the country for a year or having contact with foreigners without prior conditions for at least six months, as part of a package of restrictions slapped on him by Israeli officials fearing he may spill more secrets.
The Dimona nuclear reactor where
Vanunu worked until he was fired
Vanunu was jailed in 1986 after disclosing state secrets to Britain's Sunday Times.
The revelations embarrassed Israel, which maintains a so-called "strategic ambiguity" over its nuclear programme to try to ward off foes while avoiding a regional arms race.
The now grey-haired Vanunu denies having anything more to reveal about Israel's nuclear capabilities, but says he wants to campaign against its atomic weapons' programme.