There have been no reports of death or injuries on either side but the UN has called for restraint.
The Israeli army has said its gunners fired three rounds of artillery into southern Lebanon in retaliation for what Tel Aviv said were rocket attacks from the Lebanese side.
There were no immediate reports of casualties on either side after the incident on Wednesday.
The Israeli army said three rockets were fired from Lebanon into Israeli territory, though one fell short of the border.
The others struck near the northern town of Kiryat Shmona.
There was no immediate claim of responsibility for the rocket strike, launched from an area of south Lebanon under the sway of Iranian-backed Hezbollah guerrillas.
No one was injured in Israel other than four people who were treated for "stress symptoms", said David Adom ambulance service.
The rocket attack did start a bushfire in the Israeli hilly frontier, officials said.
The United Nations peacekeeping force in the border region, UNIFIL, urged "maximum restraint" after the exchange of fire on the day marking a year since an explosion at Beirut's port devastated swathes of the Lebanese capital and killed more than 200 people.
Head of mission Major General Stefano Del Col urged the two sides "to cease fire and to exercise maximum restraint to avoid further escalation, especially on this solemn anniversary", UNIFIL said in a statement, adding that it would investigate.
The statement came shortly after Israeli Defence Minister Benny Gantz said he had met with military leaders and "instructed the officials to deliver a firm message to UNIFIL following the attack".
Prime Minister Naftali Bennett said he and Gantz had been "briefed" on developments and were overseeing Israel's response.
The tit-for-tat attacks come as Israel faces a diplomatic crisis in which it's forcibly trying to evict dozens of Palestinians from their homes in Sheikh Jarrah neighborhood in the Occupied East Jerusalem.
The exchange of fire comes days after Israel accused Iran of carrying out an apparent drone attack on an Israeli-linked tanker off Oman that killed two crew members, and hinted at possible retaliation.
Iran denied the allegation and warned it would "respond to any possible adventurism."