Official media reported the strike on a Palestinian refugee camp.
"Fatah Sharif Abu al-Amineh, the leader of Hamas in Lebanon and a member of the movement's leadership abroad" was killed in a strike on "his home in al-Bas camp in southern Lebanon," Hamas said.
He was killed along with his wife, son and daughter in a "terrorist and criminal assassination", the statement added.
The country's official national news agency reported an air strike on a camp near the southern city of Tyre. It said it was the "first time" the camp had been targeted.
The announcement came hours after the Popular Front for the Liberation of Palestine (PFLP), a secular leftist group, announced that three of its members had been killed in a strike in Beirut's Kola neighbourhood earlier on 30 September.
Israel has repeatedly attacked Hamas members since the Gaza war began almost a year ago.
A strike in January, which a U.S. defense official says was carried out by Israel, killed Hamas deputy leader Saleh al-Arouri and six other fighters in a Hezbollah stronghold in southern Beirut.
In August, an Israeli car strike in the southern Lebanese city of Sidon killed Hamas commander Samer al-Hajj.
The official Palestinian refugee camps in Lebanon were established for Palestinians who were expelled or fled during the 1948 war, when Israel was created.
By long-standing tradition, the Lebanese army does not enter the camps and leaves the Palestinian factions to take care of security. | BGNES