Palestinian medics reported one of the medical centres, Al-Amal, was ordered evacuated by the army and two staff were wounded in a chaotic exit that has stranded teams and patients in ambulances.
Israel has launched raids on and near several Gaza hospitals since the war erupted in October, claiming that fighters have used them as bases -- charges denied by the Palestinian militants.
Palestinians living near Gaza's largest hospital, Al-Shifa, have reported hellish conditions, including corpses in the streets, constant bombardment and the rounding up of men, who are stripped to their underwear and questioned.
New images released by the military showed an Israeli battle tank rolling past one of Al-Shifa's main courtyards, which is littered with rubble and damaged vehicles, as heavily armed troops enter a building in the compound.
"We found a great quantity of armaments hidden among medical equipment, patients and people taking refuge in the hospital," a soldier identified as a special forces commander said in the video.
Israel labelled the raids underway Monday around Al-Shifa and in the Khan Yunis neighbourhood surrounding the Al-Amal hospital "precise operational activities".
But the raids have sparked major fears for the patients, medical staff and displaced people who are inside the facilities, which in some cases Israel has raided or cordoned off on more than one occasion.
The Palestinian Red Crescent said Israeli troops ordered staff and patients to evacuate Al-Amal, but the departing convoy got stuck due to debris on the road.
The groups reported the Israeli troops opened fire on staffers who tried to clear the debris, wounding two -- one of whom made it back to the convoy.
AFP has asked the military for comment.
The military said its operation in the Al-Amal neighbourhood included "raids on several terrorist infrastructure sites in the area and located explosive devices, RPGs (rocket-propelled grenades) and military equipment".
"Over 20 terrorists were eliminated in the Al-Amal area over the past day in close-quarters combat and aerial strikes," the army added.
The raid at Al-Shifa is now in its eighth day and the military reported detaining some "500 terrorists affiliated with the Hamas and Islamic Jihad terrorist organisations" and locating weapons in the area.
Israel has said that the operation will continue until the last militant is "in their hands", signalling an extended presence at Al-Shifa, which troops also raided in November.
"Because it's cautious, it will take us a couple of more days," Israeli military spokesman Rear Admiral Daniel Hagari told reporters. "How many days? I don't know -- three, four, five, approximately."
The Red Crescent on Sunday said military vehicles had also surrounded Nasser hospital, about a one-kilometre (half mile) drive from the Al-Amal medical centre, but the situation at Nasser on Monday was unclear.