Benny Gantz said the military would intervene if militants do not stop firing on northern Israel.
Time for a diplomatic solution was running out, he added.
Meanwhile, the head of the Israel Defense Forces said troops were in "very high readiness" for more fighting in the north.
"Our first task is to restore security and the sense of security to the residents in the north, and this will take time," Chief of the General Staff Lt Gen Herzi Halevi said, after conducting a "situational assessment".
Cross-border exchanges of fire have been escalating since Hamas's 7 October attacks on Israel.
On Wednesday, Hezbollah launched its highest number of cross-border attacks in a day since 8 October, security sources told Reuters.
It has led to concerns the conflict in Gaza could become wider across the region.
"The situation on Israel's northern border demands change," Mr Gantz told a press conference on Wednesday night.
"The stopwatch for a diplomatic solution is running out. If the world and the Lebanese government don't act in order to prevent the firing on Israel's northern residents, and to distance Hezbollah from the border, the IDF will do it."
Hezbollah - a Shia Muslim organisation - is designated a terrorist organisation by Western states, Israel, Gulf Arab countries and the Arab League.
Funded by Iran, it is one of the most heavily-armed, non-state military forces in the world.
In 2006, a full-blown war between Hezbollah and Israel was triggered when Hezbollah carried out a deadly cross-border raid, with Israeli troops invading southern Lebanon.