The 13-storey building was destroyed but residents and local people had been warned to evacuate, news agencies reported.
Calls for calm have come from all over the world following the escalation, which follows days of unrest in Jerusalem.
At least 31 people have died in what has amounted to some the worst violence in years.
Three people have been killed in Israeli areas while at least 28 Palestinians have been killed by Israeli air strikes, it was reported.
Israel Prime Minister Benjamin Netanyahu warned that the fighting would continue for some time.
In a nationally televised speech late on Tuesday, he said Hamas and Islamic Jihad "have paid, and will pay, a heavy price".
He added: "This campaign will take time, with determination, unity and strength."
Hamas, which controls Gaza, said it has been acting to defend Jerusalem's al-Aqsa mosque from Israeli "aggression and terrorism”.
The site, holy to Muslims and Jews, saw clashes between Israeli police and Palestinians on Monday that left hundreds injured.
The current violence, like previous rounds, including the last uprising, has been fuelled by conflicting claims over Jerusalem, which is at the emotional core of the long conflict.
In a sign of widening unrest, hundreds of residents of Arab communities across Israel staged overnight demonstrations denouncing the recent actions of Israeli security forces against Palestinians.
It was one of the largest protests by Palestinian citizens in Israel in recent years.
In the central Israeli town of Lod, police fired tear gas and stun grenades after mourners threw rocks at officers during the funeral of an Arab man allegedly shot by a Jewish resident the night before.
Thousands took part in the funeral, and police said the crowd set fire to a patrol car, a bus and a motorcycle. Two police officers were injured.
Israel and Hamas have fought three wars and numerous skirmishes since the militant group seized control of Gaza in 2007.
Recent rounds of fighting have usually ended after a few days, often helped by mediation by Qatar, Egypt and others.