The dead include 35 children and 58 women, the ministry added, while over 1,645 were wounded.
The air attacks sent residents of south Lebanon fleeing for safety northward as some public schools were turned into shelters.
"Air Force fighter jets have attacked ... about 800 Hezbollah terrorist targets in southern Lebanon and in the Bekaa area deep in Lebanon in several waves of attacks throughout the day," the Israeli air force said in a post on X.
"The IDF attacked buildings where Hezbollah hid rockets, missiles, launchers, unmanned aerial vehicles and other military infrastructure," it said, adding that it aimed to destroy the group's "capabilities and infrastructure".
For its part, Hezbollah claimed responsibility for rocket attacks targeting Israeli military sites and the Israeli military said over a million civilians were forced to seek shelter in the third-largest city Haifa.
Around 165 rockets and other projectiles launched by Hezbollah have crossed into Israel since this morning, the Israeli military added, though no casualties have yet been reported.
Israeli prime minister Benjamin Netanyahu on Monday warned of difficult days ahead, urging unity among Israelis and for Lebanese to heed Israeli evacuation orders.