Israeli authorities also announced a punitive reduction in the supply of fuel to the strip's main power station, meaning a further cut in the already rationed electricity supply.
Three rockets were fired from Gaza into southern Israel on Sunday night, the Israeli army said.
"In response, a short while ago, Israeli air force fighter jets struck a number of terror targets in a Hamas military compound in the northern Gaza Strip, including the office of a Hamas battalion commander," the Monday morning statement added.
A Palestinian security source said there had been no casualties.
A separate statement from the Israeli defence ministry said the latest fuel cut was personally ordered by Prime Minister Benjamin Netanyahu, who is also defence minister.
Netanyahu is fighting for reelection on 17 September, with critics from his right-wing power base calling for tougher action against the Islamist Hamas.
Pro-Syria Palestinian group hit in Lebanon
The strikes in Lebanon came just hours after the head of Lebanese Shiite movement Hezbollah threatened Israel after two drones fell on its Beirut stronghold in what he described as a targeted "drone attack".
The National News Agency said "three hostile strikes" after midnight hit Lebanon's eastern mountains near Qusaya town "where the Popular Front for the Liberation of Palestine - General Command has military posts".
"They responded will a barrage of anti-aircraft fire," it said.
The Popular Front has close ties with both Hezbollah and the Syrian government.
It has positions in the eastern region of Bekaa, as well as in Al-Naaemeh just south of Beirut.
Qusaya is five kilometres from the Syrian border.