The ministry reported that strikes in mountainous areas in the east "resulted in an initial death toll of two" people.
It later stated that two others were killed in a separate strike in the south around Nabatieh, with the official National News Agency (NNA) reporting an elderly woman was one of the dead.
The NNA had earlier said that "Israeli warplanes launched a series of violent strikes on the eastern mountain range" in the Bekaa region near the border with Syria.
It also reported that two Israeli strikes targeted the Hermel range in the country's northeast.
The Israeli military, meanwhile, said it had attacked Hezbollah sites in east and north Lebanon, including "a military camp and a site for the production of precision missiles" in the Bekaa valley.
The military said in a statement that it "struck several terrorist targets" in the Bekaa, including "a camp used for training Hezbollah militants".
It later announced having also struck "a Hezbollah weapons storage facility in the area of Nabatieh".
Israel has repeatedly bombed Lebanon despite a November ceasefire, which brought to an end more than a year of hostilities with the militant group Hezbollah that culminated in two months of open war.
As part of that deal, Israeli forces were to withdraw from southern Lebanon and Hezbollah was to dismantle its forces in the region.
Under US pressure and fearing an escalation of Israeli strikes, the Lebanese government has moved to begin disarming Hezbollah, a plan which the militant movement and its allies oppose.
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