The nighttime raid was triggered by fresh intelligence suggesting Hamas was using the medical facility as a base, officials said.
Israel Defence Forces spokesman Major David Baruch said: "We had intelligence that Hamas had returned to the hospital, once again using hospitals in a way that had turned itif we wanted it to be into a military target.
"We don't want it to be a military target, we're not interested in that.
"Last night at 2.31am, our forces went in. It's an ongoing operation, it isn't over yet.
"Based on high level intelligence we have actually moved in to do what we need to do there."
This raid was the fourth the IDF has conducted at Al-Shifa.
Officials later released images of weapons and bundles of cash described as "Hamas and Islamic jihad terror funds" found there.
The IDF added in a statement: "Twenty terrorists have been eliminated at the Shifa hospital thus far in various engagements, and dozens of apprehended suspects are currently in questioning."
The Israeli army had dropped leaflets around the hospital in Gaza City, warning civilians they were "in a dangerous combat zone" and urging them to move south, it was said.
Major Baruch insisted the hospital was still functioning and that surgeries had continued despite the disruption.
However, medical staff said the electricity had been cut and they were instructed not to move, preventing them from properly caring for patients.
Dr Amer Jedbeh, a surgical resident, told the BBC: "A shell hit our building on the first floor, injuring several people. One man died, we could not save him.
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