Computer expert Roy Livneh told the television station he had "easily" obtained access to the classified material, which he subsequently turned over to police.
In an allusion to Israel's nuclear arsenal, the television presenter said the documents published on the Internet "deal with special arms, which got Mordechai Vanunu 18 years in prison."
Vanunu, who worked as a technician at the Dimona nuclear facility in southern Israel, was handed an 18-year prison sentence in 1986 after giving details about Israel's secret weapons program to Britain's Sunday Times.
Although Israel has firmly adhered to a policy of "nuclear ambiguity", never confirming or denying it possessed nuclear weapons, foreign experts believe the Jewish state holds at least 200 atomic warheads.
The Israeli network refused to give further details on the reference to "special arms" nor did he release the name of the website where the documents were published, as such issues are subject to military censorship in Israel.
Among the other documents published were a report on the latest US F-16 fighter jet ordered by Israel, which says the warplane's radar system operates "below the minimum level required".
Another document contained information about a new US missile delivered to an unnamed European country, which has refused to sell the model to Israel "for political reasons".
Livneh said the leak had likely stemmed from an Israeli military official who copied the information onto his personal computer and then onto his personal website in order to have easier access.
A military spokeswoman said the leak constituted a serious "infraction of data protection", adding that an inquiry had been opened into the matter.
The television network reported that the incident was not the first time that the public had gained access to confidential military information.