The US was informed ahead of the attack, which targeted a 200-metre-long tunnel in the town of Majdal Zoun, according to the statement from Israeli Prime Minister Benjamin Netanyahu and Defence Minister Israel Katz.
The Israeli statement said the tunnel contained hundreds of weapons and launchers.
The attack comes hours after the Israeli military said it struck Hezbollah militants armed with rocket-propelled grenades and struck a rocket launcher in the Nabatieh area of southern Lebanon.
A US-brokered security agreement, which was agreed on between Lebanon and Israel on Friday, provides for a phased Israeli withdrawal from some parts of southern Lebanon, alongside the deployment of the Lebanese army. But Israeli forces would be permitted to remain in an expanded security zone for the time being.
Hezbollah leader Naim Qassem rejected the agreement, describing it as a surrender to Israel. He said the group would continue its armed resistance.
Netanyahu's statement late on Sunday said the Israeli military would remain in the security zone in southern Lebanon and will "continue to destroy terrorist infrastructure, remove threats from the northern communities, and safeguard the security of Israel's citizens".
More than a million Lebanese have been driven from their homes by the conflict that has run in parallel with the wider Iran war.
Hezbollah and Iran say Washington pledged to end hostilities in Lebanon as part of its memorandum of understanding signed two weeks ago to end the wider war.
