Gaza health officials said Israeli forces surrounded and shelled the Indonesian Hospital in the territory's northern town of Beit Lahia at dawn on Saturday, while the military reported troops were operating near the facility.
"Israeli tanks have completely surrounded the hospital, cut off electricity and shelled the hospital, targeting the second and third floors with artillery," said the facility's director, Marwan Sultan.
"There are serious risks to medical staff and patients."
In a statement, Gaza's health ministry also said Israel had targeted the upper floors, adding there were "more than 40 patients and wounded in addition to the medical staff" present.
"Heavy gunfire" towards the hospital and its courtyard had sparked a "state of great panic" among patients and staff, it added.
Contacted by AFP, the Israeli military said its troops were operating near the Indonesian Hospital.
"The troops operating in the area have been trained for the operational activity and briefed on the importance of mitigating harm to civilians and medical infrastructure," the military said in a statement to AFP.
"It is emphasised that the hospital continues to operate without disruption and in full capacity, and there was no intentional fire directed at it."
Israel launched a new offensive in northern Gaza earlier this month, saying it was targeting Hamas fighters who were regrouping there.
Gaza's civil defence agency said an Israeli strike the night before killed 33 people in Jabalia, which is nearby the Indonesian Hospital.
The UN humanitarian affairs agency on Friday continued "to sound the alarm about the increasingly dire and dangerous situation that civilians in northern Gaza are facing. Families there are trying to survive in atrocious conditions, under heavy bombardment."
Indonesian Hospital was also damaged during Israeli shelling in October, residents told AFP at the time.
Israel has come under strong international criticism for targeting hospitals in Gaza, which it has repeatedly accused of being used by Hamas militants for military purposes.