“Ibrahim Zaydat entered Lebanon on Wednesday afternoon after cutting through a small section of barbed wire at the southeastern border, and was arrested by the army,” the official was quoted as saying by AFP.
Speaking on condition of anonymity, the source said it still was not clear why Zaydat had entered Lebanon.
UN peacekeepers in south Lebanon have asked for him to be released at the request of the Israeli military command, the source said.
Lebanese authorities are questioning Zaydat and will announce later if they will release him or not, the source added.
It is rare for an Israeli civilian to cross into Lebanon.
Lebanese shepherds who stray close to the border with Israel are frequently stopped for questioning by the Israeli army but later released.
Lebanon has technically been at war with its southern neighbor since the Jewish state declared independence in 1948. Israeli citizens are banned. Even foreigners are banned if they have Israeli stamps in their passports.