The mortar attack on the kibbutz, which caused no casualties, came only hours after an Israel Air Force strike against a Qassam rocket squad killed a militant in the Hamas-ruled territory.
The mortar shell hit the roof of the clubhouse, which was vacant at the time, and caused substantial damage to the building.
The Gaza militant's death was the first due to border violence since Hamas formally declared an end to a six-month truce with Israel.
Hamas declared in a statement Friday that they would not continue a truce in Gaza that had taken effect in June.
Gaza militants Saturday fired at least 13 Qassam rockets and dozens of mortar shells into Israel, continuing the barrage of the past several days. The rocket attacks caused neither damage nor casualties, the Israel Defense Forces said.
The Al Aqsa Martyrs' Brigades, the armed wing of Palestinian President Mahmoud Abbas' Fatah movement, identified the dead man as one of its fighters. Hamas said it fired the mortars. The IDF also confirmed the militant's death.
Four Qassam rockets struck the western Negev Friday, also causing no casualties.
The IDF, meanwhile, said troops guarding Israeli farmers in fields adjacent to Gaza came under sniper fire from across the border. There were no injuries reported in any of the incidents.
In the statement posted on its Web site Friday, Hamas said Israel had breached agreements by imposing a painful blockade on Gaza, staging military strikes into the densely populated coastal strip and continuing to hunt down Hamas operatives in the West Bank.
"Since the enemy did not abide with the conditions... we hold the enemy the fully responsible for ending the truce and we confirm that the Palestinian resistance factions headed by Hamas will act," the statement said.
In light of Hamas' declaration of an end to the cease-fire, Israeli officials have warned that a military offensive in the coastal territory would be "unavoidable" if the rocket fire continues.