"Anti-tank missiles fired from Lebanon hit IDF military positions in northern Israel," the Israeli Defence Forces posted to Twitter on Sunday, Efe news reported.
"We returned fire toward the source of the attack in southern Lebanon."
Lebanon-based Shiite group Hezbollah said in a statement that it had destroyed a military vehicle in the Israeli agricultural community of Avivim and the passengers were killed or injured.
There were no initial details of injuries or damage from the Israeli army.
The army instructed Israeli residents in the affected area to stay inside anti-aircraft shelters.
The exchange of fire came after tensions between the two countries heated up in recent days due to several incidents.
The Lebanese army accused Israel of violating its airspace after an Israeli drone early Sunday dropped incendiary substance adjacent to the Blue Line between Israel and Lebanon, where the United Nations monitors an agreement on cessation of hostilities.
The Israeli army said the strikes were a result of military operations in the region, giving no further details.
On Saturday, a projectile was fired into the Shebaa Farms, a disputed land on the Israel-Lebanon border.
Lebanon's military on Wednesday said that it fired at two Israeli drones after they violated the country's airspace.
Both countries do not have diplomatic ties, and Lebanon accuses Israel of illegally crossing its borders by land, sea and air almost every day.
( With inputs from IANS )