The 13-storey building was attacked an hour and a half after residents and local people were warned to evacuate, Reuters news agency reports.
Israel's military says it is targeting militants in Gaza in response to earlier rocket attacks.
At least 30 people have died in some of the worst violence in years.
The international community has urged both sides to end the escalation, which follows days of unrest in Jerusalem.
Militants had already fired more than 400 rockets since Monday night, killing two Israelis. Health officials in Gaza report that 28 Palestinians there were killed by Israeli air strikes.
Israeli Prime Minister Benjamin Netanyahu said earlier that the main militant group, Hamas, had "crossed a red line" by firing rockets towards Jerusalem for the first time in years.
He warned that the strength and frequency of Israel's air strikes would increase and Hamas would be "hit in ways that it does not expect".
Israel says it hit at least 150 targets in Gaza in response to the earlier rocket attacks.
Hamas, which controls Gaza, says it has been acting to defend Jerusalem's al-Aqsa mosque from Israeli "aggression and terrorism" after the site, which is holy to Muslims and Jews, saw clashes between Israeli police and Palestinians on Monday that left hundreds injured.
The past few days have seen the worst violence in Jerusalem since 2017. It followed mounting Palestinian anger over the threatened eviction of families from their homes in occupied East Jerusalem by Jewish settlers. Tension had already been stoked by a month of altercations between protesters and police in the predominantly Arab part of the city.
Hamas said it had launched rockets at Tel Aviv and its suburbs in response to "the enemy's targeting of residential towers".
Video footage from the city shows rockets streaking through the night sky, some exploding as they are hit by Israeli interceptor missiles.
Pedestrians ran for shelter and diners streamed out of restaurants while others flattened themselves on pavements as the sirens sounded, according to Reuters. One woman is reported to have been killed in the town of Rishon LeZion, near Tel Aviv.
In the Tel Aviv suburb of Holon, a rocket hit an empty bus, Israeli police spokesman Mickey Rosenfeld told AFP news agency.
The rockets were launched after the destruction of the Hanadi Tower in Gaza, which houses an office used by the political leadership of Hamas, Reuters reports.
Two hours after the collapse, there were still no reports of casualties.