The Hezbollah commander is accused by Israel of being behind the deadly attack over the weekend against the Israeli-annexed Golan Heights.
"IDF (Israel's military) has carried out an attack in Beirut against a commander who was responsible for the murders of children in Majdal Shams and the murder of a large number of Israeli civilians," IDF writes in a statement.
The attack was directed against a building in a Hezbollah stronghold in Beirut's southern suburbs. An AFP photographer in Beirut reports that the top floor of an eight-story building was hit.
The target is named as Fuad Shukr. He is said to have survived the attack, according to a source close to the Hezbollah movement for AFP.
But Israel claims to have "eliminated" Shukr.
The US, which has put a price on Shukr's head, has described him as a "high-ranking adviser" to Hezbollah leader Hassan Nasrallah.
Top floor hit
Lebanon's Prime Minister Najib Mikati condemns the attack, which he describes as a "criminal act" and one in a "series of aggressive attacks where civilians have been killed in clear violations of international law". Iran, Hezbollah's ally, also condemns what the country describes as a "heinous" attack.
The US expresses concern over the situation in the region. But a full-scale war is not inevitable, adds White House press secretary Karine Jean-Pierre.
Israel has warned that it would respond with force to the weekend's attack against Majdal Shams on the Golan Heights, where twelve children between ten and sixteen years old were killed when a rocket hit a football field on Saturday.
Daily shelling
After the Israeli retaliatory attack in Beirut, Israel's Defense Minister Yoav Gallant says that Hezbollah has crossed a "red line" with the attack on Majdal Shams.
The Iran-backed militia group has denied being behind the attack, but has stated that it attacked Israeli military targets on the same day. Several analysts have speculated that it may have been a misdirected Hezbollah rocket that hit Majdal Shams.
Israel and Iran-backed Hezbollah have been shelling each other almost daily across the border since the Gaza War began after Hamas, labeled as a terrorist organization, attacked Israel in October last year.