Health officials at the Al-Ahli Arab Baptist Hospital evacuated the patients from the building on Sunday after one person said he received a call from someone who identified himself with the Israeli security shortly before the attack took place.
No casualties were reported, according to the civil emergency service.
The Israeli military said in a statement it had taken steps to reduce harm to civilians before it struck the compound, claiming it was being used by Hamas militants to plan attacks.
The hospital, an institution of the Anglican Church, was a major medical facility in Gaza City, according to the Gaza health ministry, which is now out of operation because of the attack.
"Hundreds of patients and injured people had to be evacuated in the middle of the night, and many of them are now out in the streets without medical care, which puts their lives at risk," ministry spokesperson Khalil Al-Deqran told Reuters.
Images circulating on social media, which Reuters could not immediately verify, showed dozens of people leaving the premises, with some appearing to be dragging sick relatives on hospital beds.
The Palestinian foreign ministry and Hamas condemned the attack at Al-Ahli and said in a statement that Israel was destroying Gaza's healthcare system.
Israel says Hamas systematically exploits civilian structures, including hospitals, which the militant group denies.
Israeli forces have carried out numerous raids in medical facilities in the enclave.
In October 2023, a deadly blast at a parking lot in the compound of Al-Ahli hospital was blamed by Hamas on an Israeli air strike.
An investigation by Human Rights Watch later concluded the 2023 explosion was most likely caused by a failed Palestinian rocket launch.
Sunday's strikes came hours after leaders from the Hamas group visited Cairo to hold talks with Egyptian mediators over ways to salvage the stalled ceasefire agreement.
Egypt, Qatar, and the US have stepped up efforts to bridge the gaps between Hamas and Israel.
The Baptist Church in Jerusalem and the Middle East said in a statement that 20 minutes before the attack on the hospital, the Israeli military ordered all patients, employees and displaced people to evacuate the premises.
It said the two strikes destroyed the two-storey Genetic Laboratory, damaged the Pharmacy and Emergency Department buildings, and caused collateral damage to surrounding structures, including the St Philip's church building.
"The Diocese of Jerusalem is appalled but the bombing of the hospital is now for the fifth time since the beginning of the war in 2023 - and this time was on the morning of Palm Sunday and the beginning of Holy Week," the Baptist Church said.
"We call upon all governments and people of goodwill to intervene to stop all kinds of attacks on medical and humanitarian institutions," it said in a statement.
Separate strikes in the enclave on Sunday killed at least 10 Palestinians, including the head of a police station in Khan Younis, in the southern part of the Hamas-run enclave, according to Hamas media and local health authorities.
At least eight more people, including a woman, were killed further north, according to the official Palestinian news agency WAFA.
There was no immediate Israeli comment on those reports.
The war in Gaza was triggered by Hamas' October 7, 2023, attack on southern Israel, in which 1200 people were killed and 251 taken hostage, according to Israeli tallies.
Since then, more than 50,000 Palestinians have been killed in the Israeli offensive, according to local health authorities.
Much of Gaza is in ruins and most of its population has been displaced.
