Elsewhere in Gaza, Israeli strikes killed at least 25 people, including 15 people in a single house in Gaza City, medics and the civil emergency service said.
The Palestinian health ministry said contact with staff inside the hospital in Beit Lahiya, which has been under heavy pressure from Israeli forces for weeks, had been lost.
"The occupation forces are inside the hospital now and they are burning it," ministry director Munir Al-Bursh said in a statement.
Youssef Abu El-Rish, the Hamas-appointed deputy health minister, said Israeli forces had set fire to the surgical department and laboratory and a storehouse.
Like the Indonesian and Al-Awda hospitals, Kamal Adwan has been repeatedly attacked by Israeli forces who have been attacking the northern edge of the Gaza Strip for weeks, Palestinian medical staff say.
Bursh said the army had ordered 350 people to leave Kamal Adwan for a nearby school sheltering displaced families. They included 75 patients, their companions, and 185 medical staff.
Abu El-Rish said soldiers were transferring patients and medical staff to the Indonesian Hospital, which had already been put out of action by heavy damage and had been evacuated by Israeli forces a day earlier.
Footage circulating on Palestinian and Arab media, which Reuters could not immediately verify, showed smoke rising from the area of Kamal Adwan.
Much of the area around the northern towns of Jabalia, Beit Hanoun and Beit Lahiya has been cleared of people and systematically razed, fuelling speculation that Israel intends to keep the area as a closed buffer zone after the fighting in Gaza ends.
On Thursday, health officials said five medical staff, including a pediatrician, had been killed by Israeli fire at Kamal Adwan. The Israeli military said it was unaware of a strike at the hospital and that the report of the medics' death would be examined.
In a statement, Hamas blamed Israel and the United States for the fate of the hospital's occupants.
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