Khaled Nazem Diab, a US citizen, was arrested as he entered Israel last month from the Gulf state of Qatar, where he had been working for charities.
The Israelis say he had also lived in Afghanistan and had close relations with sympathisers of the now defunct Taleban regime there.
A spokesman said Mr Diab was also "known to have contacts with organisations and activists connected to [the Palestinian militant group] Hamas".
Mr Diab is expected to be deported once the investigation is complete, though it is not known to which country.
Kenya connection
The BBC's Jeremy Cooke in Jerusalem says there is no explanation from the Israelis as to why they are releasing this information at this time.
However, it comes a day after Israeli Defence Minister Shaul Mofaz said there was clear evidence that al-Qaeda had tried unsuccessfully to infiltrate Israel.
Israeli agents are currently in Kenya investigating attacks in the holiday resort of Mombasa which killed three Israelis which have been claimed by al-Qaeda.