The pre-dawn raid on Tuesday destroyed a major part of the building and levelled a metal workshop in the Nusairat refugee camp.
Israeli occupation forces, with two dozen tanks, later invaded the town of Bait Hanun in the Gaza Strip, killing a 32-year-old Palestinian man and wounding another.
An Israeli occupation spokesman claimed the building and workshops in the missile attack were used by Palestinian resistance groups, but did not explain why they had to be blown up with missiles rather than just shut down or have their equipment confiscated.
Just a few hours earlier, Israeli soldiers also blew up an empty eight-storey building that overlooked the army outpost that was attacked earlier in the week.
But the demolition came only after soldiers razed 15 nearby Palestinian homes, leaving about 60 people homeless.
Palestinian political analyst Hasan al-Kashif said the missile strikes were actually collective punishment for a resistance attack on a settlement on Monday and an Israeli military post.
A resistance group launched home-made rockets on the Sderot town, killing a three-year-old boy and a 49-year-old man, as well as injuring at least 11 other people.
It was the first time in nearly four years of fighting that Israelis were killed by rockets from Gaza.
Hamas claimed responsibility for the attack in cooperation with al-Aqsa Martyrs' Brigades, saying they were avenging leaders and key activists killed by Israel.
Muhammad Baji, 13, was shot
dead on Monday in Khan Yunis
Several tanks rolled into northern Gaza and more armoured vehicles assembled at the Gaza border, along with dozens of troops.
The deployment may be a precursor to what Israeli security officials said could be a prolonged operation in Gaza to prevent rocket attacks on illegal Israeli settlements.
Dead and injured
It comes after a Sunday attack in which resistance fighters dug a 350m tunnel and detonated hundreds of kilos of explosives under an occupation outpost, killing a soldier and wounding five.
Following the blast, two Palestinians were killed by Israeli fire, and two more were shot dead early on Monday in Gaza.
A 13-year-old Palestinian boy also received multiple shot wounds in his legs, according to Palestinian medical sources.
Despite the upsurge in violence, Israeli Prime Minister Ariel Sharon said he remains determined to go ahead with his planned withdrawal from Gaza in 2005.
Addressing lawmakers, Sharon pledged on Monday to speed up the evacuation of settlers who are ready to leave voluntarily.
Sharon's "unilateral disengagement" plan calls for the evacuation of all Gaza Strip settlements - where some 7500 Israelis live among 1.3 million Palestinians in an area just twice the size of Washington DC.