The tower houses an office that is used by the political leadership of Gaza's Islamist rulers Hamas.Electricity in the area around the building went out after the collapse.
Residents of the tower and people living nearby had been warned to evacuate the area around an hour before the air strike, according to witnesses. It was not immediately clear if the building had been fully evacuated, or if there were casualties.
Israel had sent 80 jets to bomb Gaza on Tuesday and massed tanks on the border as rocket barrages hit Israeli towns for a second day, deepening a conflict in which at least 28 people in the Palestinian enclave and two in Israel have been killed.
The most serious outbreak of fighting since 2019 between Israel and armed factions in Gaza was triggered by clashes between Palestinians and Israeli police at Jerusalem's al-Aqsa Mosque on Monday.