The Israeli military said the official - Hassan Bdeir - was a member of a Hezbollah unit and Iran's Quds Force, and he had assisted the Palestinian group Hamas in planning a "significant and imminent terror attack against Israeli civilians".
Hezbollah confirmed that Bdeir had been killed along with his son, who was also a member of the group.
The Lebanese security source said Bdeir was a mid-ranking commander whose responsibilities included the Palestinian file.
The Lebanese health ministry said the strike killed four people - including a woman - and wounded seven others.
It marked Israel's second air strike in the Hezbollah-controlled suburb of Beirut in five days, adding to strains on the US-brokered ceasefire that ended last year's devastating conflict.
The attacks on Beirut's southern suburbs have resumed at a time of broader escalation in the region, with Israel having restarted strikes in the Gaza Strip after a two-month truce and the United States hitting the Iran-aligned Houthi rebels of Yemen in a bid to get them to stop attacking Red Sea shipping.
Hezbollah MP Ibrahim Moussawi said the Israeli attack amounted to "a major and severe aggression that has escalated the situation to an entirely different level".
Speaking in a televised statement after visiting the building that was struck, he called on the Lebanese state to "activate the highest level of diplomacy to find solutions".
Israeli Foreign Minister Gideon Saar said the eliminated Hezbollah operative posed "a real and immediate threat".
"We expect Lebanon to take action to uproot terrorist organisations acting within its borders against Israel," he said.
Israel dealt severe blows to Hezbollah in the war, killing thousands of its fighters, destroying much of its arsenal and eliminating its top leadership, including Hassan Nasrallah.
Hezbollah has denied any role in recent rocket attacks from Lebanon towards Israel, including one that prompted Israel to carry out an air strike on the southern suburbs last Friday.
Tuesday's strike in the early hours appeared to have damaged the upper three floors of a building, a Reuters reporter at the scene said, with the balconies of those floors blown out.
The glass on the floors below was intact, indicating a targeted strike.
Ambulances were at the scene as families fled to other parts of Beirut.
There was no advance warning, in contrast to the attack on Friday when the Israeli military announced which building it intended to hit and ordered residents to leave the area.
Lebanese President Joseph Aoun condemned the latest air strike, calling it a "dangerous warning" that signals premeditated intentions against Lebanon, which would intensify diplomatic outreach and mobilise international allies.
Lebanese Prime Minister Nawaf Salam said the strike was a flagrant breach of a United Nations Security Council Resolution upon which the ceasefire was based, and the ceasefire arrangement.
The ceasefire agreement demanded that southern Lebanon be free of Hezbollah fighters and weapons, that Lebanese troops deploy into the area and that Israeli troops withdraw.
But each side accuses the other of failing to implement the terms fully.
Israel says Hezbollah still has infrastructure in the south while Lebanon and Hezbollah say Israel is occupying Lebanese soil by not withdrawing from five hilltop positions.
