The attack in Beirut was followed by others in the city's southern suburbs after calls by the Israeli military to evacuate the area.
Israel has not commented on the strike in central Beirut, while Hezbollah has yet to mention it.
Rescue operations were underway in the area on Saturday morning, with an excavator removing the rubble of the eight-storey building, and a fire truck and civil defence rescuers stationed nearby.
"The strike was so strong it felt like the building was about to fall on our heads," said Samir, 60, who lives in a building facing the one that was destroyed.
He said he fled his home in the middle of the night with his wife and children.
"We saw two dead people on the ground... The children started crying and their mother cried even more," he told AFP.
The Israeli strike, which hit the working-class Basta neighbourhood, killed at least 11 people and wounded 63, the health ministry said, adding it had also left behind "a large amount of body parts that are being identified".
"The final death toll will be determined after DNA tests are carried out," the ministry said in a statement.
The state-run National News Agency said Israeli jets had launched six missiles at the structure, causing "widespread destruction in buildings" nearby.
The predawn attack in Basta was not preceded by an evacuation warning from Israel's military. Similar strikes carried out without warning outside of Hezbollah's traditional bastions have tended to target high-level members.
Another strike hit the neighbourhood of Hadath in Beirut's southern suburbs, which are a stronghold of Hezbollah.
The Israeli military said it had struck Hezbollah targets in the city's southern suburbs including "several Hezbollah command centres".
Israel stepped up its campaign against the Iran-backed group in late September, targeting its strongholds in the east and south as well as south Beirut, and later sending in ground troops after nearly a year of limited cross-border exchanges of fire.
Lebanon's health ministry says at least 3,645 people have been killed since October 2023, when Hezbollah began trading fire with Israel in solidarity with its Palestinian ally Hamas. Most of the deaths have been since September this year.
Gaza hospitals struggling
The war in Gaza was triggered by Hamas's unprecedented October 7, 2023 attack on Israel, which resulted in the deaths of 1,206 people, mostly civilians, according to an AFP tally of Israeli official figures.
At least 44,056 people have been killed in Gaza during more than 13 months of war, most of them civilians, according to figures from Gaza's health ministry which the United Nations considers reliable.
Civil defence agency spokesman Mahmud Bassal told AFP on Saturday that "19 people were killed and more than 40 wounded" by predawn Israeli air strikes and tank fire.
Umm Muhammad Abu Sabla, the sister of one of the victims of Saturday's strikes, told AFP she rushed to the scene to find "people carrying body parts from under the rubble".
"Our entire life is misery. Let them kill us all so we can be relieved from this suffering," the 62-year-old said in the main southern city of Khan Yunis.
The war has created a humanitarian crisis in the besieged territory, where people are experiencing acute shortages of food, fuel and medicine.
Marwan al-Hams, director of Gaza's field hospitals, told reporters on Friday that all hospitals in the Palestinian territory "will stop working or reduce their services within 48 hours due to the occupation's (Israel's) obstruction of fuel entry".
The United Nations and others have repeatedly decried humanitarian conditions, particularly in northern Gaza, where Israel said Friday it had killed two commanders involved in Hamas's October 7, 2023 attack.
Vowing to stop Hamas from regrouping, Israel on October 6 began a renewed air and ground operation in the north.
Gaza's health ministry says the operation has killed thousands.
The UN says more than 100,000 have been displaced from the area, and an official told the Security Council last week that people "are effectively starving".
'Absurd' warrants
The Hague-based International Criminal Court announced on Thursday that it had issued arrest warrants for Israeli Prime Minister Benjamin Netanyahu and former defence minister Yoav Gallant over their conduct of the war in Gaza.
The court said there were "reasonable grounds" to believe the pair bore "criminal responsibility" for the war crime of starvation as a method of warfare and crimes against humanity, including over "the lack of food, water, electricity and fuel, and specific medical supplies".
A furious Netanyahu said: "Israel rejects with disgust the absurd and false actions and accusations made against it."
Israel said it killed Deif in July, but Hamas has not confirmed his death.
