Health officials at the al-Ahli Arab Hospital removed patients from the building after a phone call from someone who identified himself as Israeli security shortly before the attack.
No casualties were reported in the strike.
The Israeli military said in a statement that it had taken steps to reduce harm to civilians before it struck the compound, which it said was being used by Hamas militants to plan attacks.
Hamas rejected the accusation and called for an international investigation.
The hospital - an institution run by the Anglican Church in Jerusalem - was no longer operational, according to Gaza's health ministry.
"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 spokesman Khalil al-Deqran said.
Sunday's strikes came as Hamas leaders began a fresh round of talks in Cairo in a bid to salvage a stalled ceasefire agreement with Israel as Egypt, Qatar and the United States attempted to bridge gaps between the sides.
Reuters footage showed significant destruction in and outside the hospital compound's church, and patients who could not leave.
"The scene was scary. From last night until now, I haven't slept a single minute out of fear. All night, glass was shattering over us inside," said an injured man, Mohammed Abu Nasser.
The Episcopal Church in Jerusalem said the warning to evacuate the hospital came 20 minutes before the strike that destroyed the two-storey genetic laboratory, and damaged the pharmacy and emergency department buildings and other surrounding structures.
"We call upon all governments and people of goodwill to intervene to stop all kinds of attacks on medical and humanitarian institutions," the church said in a statement.
The Palestinian foreign ministry and Hamas condemned the attack, saying Israel was destroying the Gaza Strip'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 Gaza Strip.
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.
Israel said a failed rocket launch by the Palestinian Islamic Jihad group had caused the blast.
The militant group denied it was responsible.
An investigation by Human Rights Watch concluded the explosion was most likely caused by a failed Palestinian rocket launch.
Separate strikes in the enclave on Sunday killed at least 30 Palestinians, including the head of a police station in Khan Younis, in the southern part of the Hamas-run enclave, according to Hamas and health authorities.
Six brothers were killed when an Israeli strike hit their car in Deir al-Balah in central Gaza Strip, medics said.
Later on Sunday, the Israeli military said it had located and destroyed a 1.2km underground tunnel used by militants in the northern Gaza Strip.
It said it struck several militants identified as planting a bomb near the Israeli soldiers carrying out the operation to demolish the tunnel.
The armed wing of Hamas, meanwhile, said its fighters detonated bombs they had planted in a house in eastern Rafah, in the south of the enclave, after Israeli soldiers entered it.
The Gaza Strip war 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 50,900 Palestinians have been killed in the Israeli offensive, according to local health authorities.
