Israel's military announced late on Tuesday it had killed Shukr, whom it named as Hezbollah's most senior commander and whom it blamed for an attack at the weekend that left a dozen youngsters dead in the Israeli-occupied Golan Heights.
Iran-backed Hezbollah has denied any involvement in Saturday's attack.
Israeli Defence Minister Yoav Gallant said Shukr "has the blood of many Israelis on his hands. Tonight, we have shown that the blood of our people has a price, and that there is no place out of reach for our forces to this end".
A senior security source from another country in the region confirmed Shukr had died of his wounds.
At least two women and two children were also killed, medical and security sources said.
Hezbollah's statement on Wednesday said Israel had attacked a residential building in the southern suburbs of Beirut, a stronghold for the group, and "a number of citizens" had been killed and others wounded.
A weekend rocket attack left a dozen youngsters dead in the Israeli-occupied Golan Heights. (AP PHOTO)
It said Shukr "was present in this building at the time" but the group was still awaiting definitive results on his fate.
Shukr was an adviser to Hezbollah leader Sayyed Hassan Nasrallah, according to Hezbollah sources and to the Israeli military's announcement of his killing.
His apparent killing marks the most senior Hezbollah commander to have been killed in nearly 10 months of exchanges of fire between the Israeli military and Hezbollah, taking place in parallel with the Gaza War.
The strike on Beirut came shortly before the assassination of Hamas leader Ismail Haniyeh early on Wednesday in Iran, in a development that has further fanned fears of wider regional escalation. Hezbollah is an ally of Hamas.
The attack appeared to have shorn off the top corner of a multi-storey building and scattered bits of charred debris onto the surroundings buildings and streets.
Lebanese ministers and MPs visited the scene on Wednesday.
Speaking from the ruins, Hezbollah parliamentarian Ali Ammar condemned the strike on Dahiyeh as well as the killing of Haniyeh in Tehran. Israel has made no comment on Haniyeh's assassination.
"This enemy (Israel) demands war and we are up for it, God willing, we are up for it," Ammar said.
Lebanon's cabinet held an emergency meeting on Wednesday morning.
Information Minister Ziad Makary later condemned the strike and said retaliation by Hezbollah was anticipated but the government was worried the situation could "spiral".
"Lebanon does not want war," he said, adding the government would engage in diplomatic efforts to calm tensions.
The weekend killings in Majdal Shams set off a diplomatic flurry led by the United States to contain Israel's response by urging it not to strike Beirut, its southern suburbs or civilian infrastructure, five people with knowledge of the efforts said.
