The raid on the Beirut suburb, an overcrowded residential area that is also a Hezbollah bastion, killed five civilians -- three women and two children, according to Lebanon's health ministry.
It was followed by another strike, hours later, which killed Hezbollah ally Hamas's political leader Ismail Haniyeh in Tehran, further stoking fears that the Gaza war could spill over.
UN Secrertary-General Antonio Guterres denounced the two strikes as a "dangerous escalation at a moment in which all efforts should instead be leading to a ceasefire in Gaza" and "the release of all Israeli hostages", his spokesman Stephane Dujarric said in a statement.
Lina Khatib, an associate fellow and Middle East expert at Chatham House, told AFP: "Even if the actors involved do not intend for all-out war to break out, every escalation increases the risk of things spiralling out of control."
The source, who requested anonymity due to the sensitivity of the matter, said "Shukr's body has been found under the rubble of the targeted building," after Israel's military said it had killed the commander on Tuesday.
AFP photographers saw rescuers combing through the rubble almost immediately after explosions rocked the Lebanese capital on Tuesday evening.
The Israeli military said its strike had "eliminated" Shukr, who it blamed for carrying out a weekend rocket attack on the annexed Golan Heights that killed 12 children in a Druze Arab town.
Hezbollah has denied responsibility for Saturday's deadly rocket strike on the Druze Arab town of Majdal Shams in the Israeli-annexed Golan Heights, though the Iran-backed group claimed multiple strikes on Israeli military positions that day.
The Israeli army has described Shukr as Hezbollah's "most senior military commander" and "right-hand man" to the group's chief Hassan Nasrallah.
Army chief Herzi Halevi said on Wednesday that Israel would "not let the situation return to having (Hezbollah) present on the border" where there have been near-daily exchanges of fire between the group and Israel.
Ahead of the strike, Hezbollah evacuated some of its positions in southern and eastern Lebanon in anticipation of Israeli retaliation.
'I could lose my children'
Earlier on Wednesday, Hezbollah confirmed Shukr was inside the targeted building but said his fate was still unknown.
Hezbollah said in a statement that "the great jihadist commander brother Fuad Shukr (Hajj Mohsen) was present" in the targeted building with rescue teams "working... to remove the rubble... and we are still waiting for the results of this operation regarding the fate of the great commander".
At the procession in southern Beirut, some carried photographs of the two dead siblings while others held up Hezbollah's flag.
"I feel very angry because the... lives of our children are becoming very cheap," said Aya Ahmed, 38, a friend of the two killed children's mother.
"Every mother now is thinking: I could lose my children at any moment because the Israelis have a license to kill," said Ahmed.
In 2017, the US Treasury offered $5 million for information on Shukr, in his early sixties, describing him as "a senior adviser" to Hezbollah leader Hassan Nasrallah.
The Treasury said he had "a central role" in the deadly 1983 bombing of the US Marine Corps barracks in Beirut.
