Mushtaha established Hamas's General Security Mechanism along with Hamas leader Yahya Sinwar, the IDF reported.
Syrian state television earlier said that one of its presenters was killed in an Israeli strike on Damascus.
The IDF had warned it would strike specific buildings in the neighborhood, a densely populated district south of the Lebanese capital, as fears grow of a looming ground invasion.
Prime Minister Benjamin Netanyahu approved the operation from onboard the Wing of Zion plane while en route to the US, the Prime Minister's Office stated.
After many months where it seemed Israel was only responding proportionately to Hezbollah’s attacks, it now appears that Israel is turning the tables.
The IDF confirmed several airstrikes on Hezbollah targets in southern Lebanon, following a series of rocket launches from Lebanese territory that threatened Israeli civilians.
The targeted facility had been operational for over a decade and was also targeted by Israel last year.
The “Amr Ibn al-As” School, located in northern Gaza, was reportedly used by Hamas to plan and launch attacks both on Israeli forces in the Gaza Strip and on Israeli territory.
Hezbollah announced that it had launched an attack on Israel in retaliation for the killing of Fuad Shukr in Beirut.
Explosions have been heard above Hama, Syrian media reported on Friday night while attributing the noise to an Israeli airstrike.