He declined to say how many were detected, when they reached Israeli territory and how they would be destroyed.
The army said the operation was for now confined to Israel and did not extend into Lebanon, where the tunnels originated. "This activity is another example of the negative effects of Iranian entrenchment in the region".
It later published a photograph of a tunnel that it said it had uncovered.
The tunnel's exit point was found in a patch of farmland southwest of the pastoral Israeli border town of Metula, the military said.
"The situation in UNIFIL's area of operation remains calm", Malene Jensen, a spokeswoman for the United Nations mission which monitors the border region, said in a statement. The tunnels evidently were meant as the surprise element of that plan, Israel Hayom reports.
It has since boasted re-building its tunnel network but never clearly stated they were to be used for cross-border attacks.
He said the military "holds the Lebanese government responsible for all activities perpetrated in Lebanon towards Israel".
Additional IDF troops were deployed to northern Israel as a precaution against potential attacks by Hezbollah, but no reservists were called up. Israel has also reportedly carried out killings against Hezbollah figures.
"In 2012, we identified the "Conquering the Galilee" plan (Hezbollah leader) Nasrallah has been talking about, and it includes a surprising component of offensive tunnels". He did not explain why the operation was launched now.
Local residents told Israeli media they had been hearing digging noises for years and had reported their suspicions to the military.More news: Qualcomm Rules Out Another Bid for NXP After China Opens Door
More news: Ex-Players pay tribute to OSU coach Urban Meyer
More news: Arsenal and Tottenham charged over player conduct in north London derby
The current operation was likely part of the discussions between Israeli Prime Minister Benjamin Netanyahu and US Secretary of State Mike Pompeo Monday evening in Brussels. "Whoever tries to attack the state of Israel - will pay a heavy price".
There was no immediate comment from Hezbollah and its Al-Manar TV did not make any mention of the Israeli operation.
Hours after launching "Operation Northern Shield" on Tuesday morning, the IDF said it was readying to destroy a Hezbollah tunnel burrowed some 40 meters into Israeli territory.
Conricus said that while the army has enhanced its presence in the north, it has not summoned reserve soldiers. On its Twitter account, the Lebanese army said its forces were "closely" following developments and were "totally prepared to confront any sudden occurrence".
The tunnels were dug "from within civilian houses in Lebanon into Israel", Conricus said, calling it a tactic that was born out of the end of the 2006 war.
Netanyahu has pledged to stop arch-foe Iran from entrenching itself militarily in Syria and to keep it from transferring advanced weapons to its ally Hizbullah in Lebanon.
Before his departure, Netanyahu hinted at the Israel operation. Amid the crisis he took on the defence portfolio from his resigning minister and promised to pursue a hard line against Israel's enemies during what he described as a "complex" security situation.
Israel also faces terror tunnels in the south from the Hamas terror organization in Gaza.
Hezbollah, which possesses one of the most powerful militias in the region, has threatened to attack Israel with its vast rocket arsenal if war breaks out. Israel is on high alert for any possible Hezbollah reaction.
Neither side appears interested in another full-fledged confrontation like the 2006 war, but any skirmish could spark an all-out conflict.