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The World Health Organization (WHO) says Al-Shifa hospital in Gaza City "is not functioning as a hospital anymore".
The WHO says "constant gunfire and bombings in the area have exacerbated the already critical circumstances".
The BBC has been sent pictures of at least 20 newborn babies being kept in a surgical theatre at the site.
The Israeli military says it has agreed to help evacuate babies from the hospital to a "safer" facility but denies Al-Shifa has lost power.
Israel's president Isaac Herzog says Hamas has its base underneath the building - something Hamas denies. The Israeli military says it is not hitting the hospital during fighting.
Gaza's second biggest hospital, Al-Quds, is also reported by a charity to have run out of fuel.
Israel began striking Gaza after the Hamas attacks on 7 October, which saw 1,200 people killed and more than 200 taken hostage.
The Hamas-run health ministry says more than 11,000 people have been killed in Gaza since - of whom more than 4,500 were children.
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