Israel attacked Beirut on Sunday in what it said was a response to Hezbollah rocket fire, on the day a US-Iran deal could be signed.
In a joint statement, Prime Minister Benjamin Netanyahu and Defence Minister Israel Katz said the Israeli military had targeted sites belonging to Hezbollah in the Dahiyeh district of Lebanon's capital.
"Israel will not tolerate firing into its territory," they said. The military said the attack was a "precise strike" on a Hezbollah command centre.
Lebanese state media said a strike hit the Ghobeiry neighbourhood, killing one person and wounding four others.
The Israeli army had said earlier on Sunday that Hezbollah launched three projectiles towards northern Israeli communities in what it described as a ceasefire violation. There was no immediate comment from Hezbollah on the Israeli claim.
The projectiles fell near the communities of Shomera and Shlomi, the military added. It said this was in addition to two projectiles that crossed into the territory over the weekend.
Israel and Hezbollah regularly exchange fire in southern Lebanon but the capital - including districts seen as bastions of the Iran-backed group - has been relatively spared of late, having been struck only twice since mid-April.
Israel's military struck Beirut's southern suburbs last Sunday, hitting apartments in two buildings. That led to one of the war's biggest flare-ups in weeks, as Iran launched attacks on Israel in protest at the war in Lebanon.
The regional situation had cooled since then, with the US and Iran appearing close to clinching an initial peace deal. US and Pakistani leaders had signalled that a signing could come as soon as Sunday.
Iran has long made the cessation of fighting in Lebanon a condition for any wider agreement with the United States.
Also on Sunday, the Israeli military issued displacement orders for people in more than two dozen villages in southern Lebanon, saying it was set to act against Hezbollah targets in the area.
Earlier this month, US President Donald Trump said Hezbollah and Israel had agreed to stop attacking each other after weeks of intense fighting and fears the Israeli military would increase attacks on Beirut.
Mr Trump said he secured a pledge from Iran-backed Hezbollah to refrain from attacks on Israel, and that Mr Netanyahu said his forces would not push deeper into Lebanon.
Almost 3,700 people have been killed in Lebanon by Israeli attacks since March 2, 730 of them women, children or medics, according to Lebanon's health ministry, while authorities say some 1.2 million people have been displaced in Lebanon.
Hezbollah entered the war on March 2, saying it was retaliating for the killing of Iran's supreme leader at the start of the conflict.
Since then, 28 Israeli soldiers have been killed in combat in Lebanon, according to a Reuters tally of Israeli military announcements, while four civilians have been killed in Hezbollah attacks.
