The strike came as US Secretary of State Antony Blinken said Israel had accomplished its objective of "effectively dismantling" Hamas, and that negotiations over a ceasefire and the release of dozens of Israeli hostages would resume "in the coming days".
Another 42 people were wounded in the strike in the built-up Nuseirat refugee camp, according to the Awda Hospital, which received the casualties.
Among the dead were 13 children under the age of 18 and three women, according to the hospital's records.
The Israeli military said it targeted Hamas militants inside the school, without providing evidence.
Israel has carried out strikes on several schools-turned-shelters in recent months, saying it precisely targets militants hiding out among civilians.
The strikes often kill women and children.
Blinken, speaking to reporters in Qatar, which has served as a key mediator between Israel and Hamas, said negotiators would soon return to Doha to renew the long-stalled talks even as it remained uncertain whether Hamas was willing to re-engage.
"What we really have to determine is whether Hamas is prepared to engage," Blinken said on his eleventh visit to the region since the start of the war.
The Israeli prime minister's office also said the head of the Mossad, the country's spy agency, would head to Qatar on Sunday for the new round of in-person talks with the CIA director Bill Burns and Qatari officials.
The United States has hoped to revive the negotiations since Israeli forces killed top Hamas leader Yahya Sinwar in Gaza last week, but neither side has shown signs of moderating its demands from months of negotiations that sputtered to a halt over the summer.
Blinken also announced an additional $US135 million ($A203 million) in US aid to the Palestinians, while again urging Israel to allow more assistance to enter the territory.
Health workers in besieged northern Gaza meanwhile warned of a catastrophic situation there, where Israel has been waging an air and ground offensive for more than two weeks.
Humanitarian access in Gaza remains restricted.— United Nations (@UN) @UNOCHA says in the last 3 weeks, only 4 out of 70 coordinated aid movements to the north via checkpoints were permitted by Israeli authorities.Without humanitarian access, lives hang in the balance. https://t.co/o0EzM6GtYv pic.twitter.com/fKAErKP73ZOctober 22, 2024
Hundreds of people have been killed and tens of thousands have fled their homes in northern Gaza in recent days.
The military says it is battling Hamas fighters who regrouped in the north, which was one of the first targets of the ground offensive at the start of the war.
Dr Hossam Abu Safiyeh, the director of the Kamal Adwan Hospital in the north, said in a video message released on Wednesday that some 150 wounded people were being treated there, including 14 children in intensive care or the neonatal department.
"There is a very large number of wounded people, and we lose at least one person every hour because of the lack of medical supplies and medical staff," he said.
"Our ambulances can't transfer wounded people," he said.
"Those who can arrive by themselves to the hospital receive care, but those who don't just die in the streets."
Footage shared with The Associated Press shows medical staff tending to premature babies and several older children in hospital beds, some with severe burns.
One child is seen attached to a breathing machine, with bandages on her face and flies hovering over her.
"We are providing the bare minimum to patients.
Everyone is paying the price of what is happening now in northern Gaza," Abu Safiyeh said.
Kamal Adwan is one of three hospitals in the north left largely inaccessible because of the fighting.
The war has gutted the health system across Gaza, with only 16 of 39 hospitals even partially functioning, according to the World Health Organization.
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