Three missiles caused the building's roof to collapse on Sunday afternoon, forcing dozens of screaming women to call for help from their balconies.
Residents said at least two people had been seriously injured though no official source has yet provided details.
But Israeli occupation forces said the block of flats housed a local radio station with links to the resistance movement Hamas.
The Ayyam newspaper also owns an office in the building.
The missile attack was a collective punishment for an earlier Palestinian shooting of illegal Israeli settlers on their way to protest any withdrawal.
Two Palestinian groups claimed responsibility for the killing of five Israeli settlers in a shooting attack in the Gaza Strip.
Islamic Jihad and the Popular Resistance Committees said they jointly attacked a car which was carrying a woman and her four daughters on a restricted-access road from Israel to their colony.
It was the first killing of settlers in Gaza in more than a year.
The attack comes as members of Prime Minister Ariel Sharon's Likud party voted on a withdrawal of settlers and troops from occupied Gaza.