The IDF said several anti-tank missiles were fired from Lebanon, scoring hits, and Israeli forces were responding.
The IDF ordered border towns in northern Israel to open their public bomb shelters.
Communities up to 2.5 miles from the Lebanese border were given the directive, amid fears of a Hezbollah attack.
Earlier, the Lebanese military said an Israeli drone, which violated Lebanon’s airspace, dropped incendiary material and sparked a fire in a pine forest by the border on Sunday.
The fires near the border in Lebanon “originate with operations by our forces in the area,” the IDF said in a statement without elaborating.
The Lebanese army statement said it was following up with U.N. peacekeepers but gave no further details.
Residents and security sources at the border in south Lebanon say Israel has in recent days fired flare bombs into the Israeli-held Shebaa farms along the border.
Lebanese state news agency NNA said Israeli forces fired flare bombs there on Shabbos – a tactic sometimes used to burn away brush to prevent an ambush.
The IDF said over the weekend that it had ordered extra forces to deploy near the border, amid rising tensions with Lebanon’s Hezbollah movement.
The leader of Iran-backed Hezbollah, Sayyed Hassan Nasrallah, said his field commanders were prepared to retaliate to a drone attack in Beirut’s suburbs a week ago, which he has blamed on Israel.
Lebanese soldiers, who do not have air defense systems, opened fire at Israeli drones in southern Lebanon earlier last week.
Israeli aircraft regularly enter Lebanese airspace, but it is rare for Lebanon’s army to target them. Beirut has sent several complaints to the United Nations before about Israeli drones and jets breaching its airspace.