The Israeli occupation army said it had "targeted a building used by the al-Aqsa Martyrs' Brigades terror organisation".
The brigades are part of Fatah, the movement of Mahmoud Abbas, the Palestinian president.
There were no immediate reports of casualties.
Missiles also struck roads in the northern Gaza Strip that Israel said were used by armed groups on their way to fire rockets across the border.
"The objective of targeting these access routes is to prevent the passage of terrorists," an Israeli army statement said on Monday.
The al-Aqsa group has been behind much of the firing of makeshift rockets from the Gaza Strip into Israel that prompted the Israeli declaration of a "no-go" zone in northern Gaza last week.
Violence has been on the increase since Israel withdrew from Gaza in September after 38 years of occupation.
Resistance groups have said that as of 1 January, they are no longer abiding by a promise they made to follow a "period of calm". They say rocket attacks are a response to Israeli military actions in Gaza and the occupied West Bank.
Abbas has appealed to the factions to exercise restraint. Israel rules out talks on Palestinian statehood until the groups are disarmed, a process that is meant to start under a US-backed peace plan.
But Israel has failed to meet its own promise under the plan to freeze settlement building in the West Bank.
Meanwhile, about 200 police officers stormed government offices in the southern Gaza Strip town of Rafah on Monday to protest at the failure of the Palestinian Authority (PA) to
fight growing lawlessness, witnesses said.
The incident was the latest sign of chaos in Gaza, which has suffered growing internal unrest recently.
About 200 officers protested at
the PA failure over lawlessness
Firing into the air as they ran through the streets, the police officers raided government offices, courthouses, an election office and the municipality building in Rafah.
They smashed windows at the Interior Ministry building and forced the staff to leave.
One officer said: "We are calling on all officers to take off their uniforms because the Palestinian Authority has tied the hands of policemen, preventing us from implementing law and order."