The army said the base, south of Beirut, belonged to the Popular Front for the Liberation of Palestine, a small group that has waged a decades-long fight against the Jewish state.
“This is in response to the firing of projectile rockets last night toward Israeli communities,” the army said early on Wednesday.
It said it viewed such attacks with “extreme severity” and held Lebanon responsible.
Late on Tuesday, seven Katyusha rockets were fired from southern Lebanon into northern Israel, Lebanese police said. No injuries were reported.
Three projectiles landed in the town of Kiryat Shemona, near the Lebanese border, causing some damage, the Israeli army said, according to the Associated Press.
Israeli Channel Two television showed the remains of what appeared to be a Katyusha rocket, along with pictures of holes in the ground and in the side of a home.
Lebanese police told AFP that two rockets were fired from an area 20km southeast of Tyre near the border and five others from Aadaysse hill.
There was no immediate claim of responsibility for the rocket attack.
A Hizb Allah spokesman in Beirut denied any knowledge of the attack, and Sultan Abu Iynayn, in charge of the Palestinian Fatah movement in Lebanon, denied any involvement by Palestinians in a statement to a local television station.
Hizb Allah and Palestinian fighters operate in nearby southern Lebanon.
Last month, Israeli fighter jets attacked a Hizb Allah command post in south Lebanon, a day after Hizb Allah rocket and mortar attacks wounded 11 Israeli soldiers and damaged a house in an Israeli border community.
Israel withdrew from an occupied enclave in southern Lebanon in 2000.
While fighting in the area has dropped since then, the border remains tense, and Hizb Allah frequently targets Israeli troops in the disputed Shebaa Farms area.
Lebanon and Syria say Shebaa Farms is Lebanese territory, but UN cartographers who surveyed the border after the Israeli withdrawal said it belonged to that part of Syria which Israel had occupied since the 1967 Middle East war.
Israel says it will discuss control of the area only in future peace talks with Syria.