Al-Nuseirat in central Gaza on Saturday, the territory's health ministry and the official Palestinian news agency said.
The Israeli military said it was looking into the report.
The health ministry said the attack on the school killed at least 16 people and wounded more than 50.
Mahmoud Basal, spokesman of the Gaza Civil Emergency Service, said the number of dead could rise because many of the wounded were in critical condition.
The attack on the school meant no place in the enclave was safe for families who leave their houses to seek shelters, he said in a statement.
Al-Nuseirat, one of Gaza Strip's eight historic refugee camps, was the site of stepped-up Israeli bombardment on Saturday. An air strike earlier on a house in the camp killed at least 10 people and wounded many others, according to medics.
In its daily update of people killed in the nearly nine-month-old war, the Gaza health ministry said Israeli military strikes across the enclave killed at least 29 Palestinians in the past 24 hours and wounded 100 others.
Among those killed in separate air strikes were five local journalists, raising the toll of journalists killed since Oct. 7 to 158, according to the Hamas-led Gaza government media office.
Gaza health authorities say more than 38,000 Palestinians have been killed in Israel's offensive. Israel launched its operation, aimed at eliminating the militant Islamist group Hamas, in response to a Hamas-led assault on Israel on Oct. 7 in which 1,200 people were killed and over 250 taken hostage,