The violence came as fears of an all-out regional war mount following the killings last week of a senior Hezbollah commander in Lebanon and Hamas' top political leader in Iran.
The Iranian-backed Hezbollah said in a statement it targeted a military base in northern Israel in response to "attacks and assassinations" carried out by Israel in several villages in south Lebanon.
The attack did not appear to be part of a more intense retaliation expected in response to the killing of Hezbollah commander Fouad Shukur in Beirut last week.
Israel and Hezbollah have exchanged near-daily strikes for the past 10 months against the backdrop of the war in Gaza, but they have previously kept the conflict at a low level that had not escalated into full-on war.
Last week's assassinations of Hamas political leader Ismail Haniyeh in Iran's capital, Tehran, and Hezbollah commander Shukur in Beirut raised tensions in the region. Israel has been bracing for a retaliation from Iran and its allied militias.
Gen. Hossein Salami, the head of Iran's paramilitary Revolutionary Guard, threatened Israel on Monday over the assassination of Haniyeh, warning that Israel was "digging its own grave" with its actions in its war against Hamas.
"They will see the result of their mistake. They will see when, how and where they will get their response," Salami said in a speech.