Youssef Sweilam, 23, from the occupied West Bank, was contacted by Hezbollah operatives on social media and "instructed to form a terror cell with the intent to carry out a kidnapping from Israel into Lebanon," the army said.
In addition, his minders "instructed him to gather information regarding (Israeli) military bases, security checkpoints, and passages, specifically in the area of the Old City of Jerusalem," the English-language statement said.
It did not say when he was arrested but said the plans were foiled before he began to enact them.
Lebanon and Israel are still officially at war although the border area has been relatively calm in recent years.
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Hezbollah and Israel scuffle intermittently in the disputed border area between the two countries.
The powerful Shiite Muslim group has targeted Israeli army patrols along the border in southern Lebanon in response to strikes against its members, sometimes in Syria where Hezbollah is supporting President Bashar al-Assad.
A 34-day conflict in 2006 led to the deaths of 1,200 people in Lebanon, mainly civilians, and 160 Israelis, mostly soldiers.