The newborns had been in north Gaza's Al Shifa hospital, where several others died after their incubators were knocked out amid a collapse of medical services during Israel's military assault on Gaza City.
Israeli forces seized Shifa last week to search for what they said was a Hamas tunnel network built underneath.
Hundreds of patients, medical staff and displaced people left Shifa at the weekend, with doctors saying they were ejected by troops and Israel saying the departures were voluntary.
Live footage aired by Egypt's Al Qahera TV showed medical staff carefully lifting infants from inside an ambulance and placing them in mobile incubators, which were then wheeled across a car park towards other ambulances.
The babies were transported on Sunday to a hospital in Rafah, on the southern border of Hamas-ruled Gaza, so their condition could be stabilised ahead of transfer to Egypt.
WHO chief Tedros Adhanom Ghebreyesus said 12 had been flown on to Cairo.
All of the relocated babies were "fighting serious infections," a WHO representative said.
A group of prematurely born babies has been transferred to Egypt from Gaza's Al-Shifa hospital.
Eight infants have died since doctors at Shifa originally raised an international alarm this month about 39 premature babies at risk from a lack of infection control, clean water and medicines in the neo-natal ward.
At the Indonesian Hospital, funded by the government in Jakarta, Gaza's health ministry said at least 12 Palestinians were killed and dozens wounded by firing into the complex encircled by Israeli tanks.
Health officials said 700 patients along with staff were under Israeli fire.
The Palestinian news agency WAFA said the facility in the northeast Gaza town of Beit Lahia had been hit by artillery rounds.
Hospital staff denied there were any armed militants on the premises.
WHO chief Tedros said he was "appalled" by the attack that he too said had killed 12 people, including patients, citing unspecified reports.
The Israeli Defence Forces (IDF) said troops had fired back at fighters in the hospital while taking "numerous measures to minimise harm" to non-combatants.
"Overnight, terrorists opened fire from within the Indonesian Hospital in Gaza toward IDF troops operating outside the hospital," the IDF told Reuters.
"In response, IDF troops directly targeted the specific source of enemy fire. No shells were fired toward the hospital."
Like all other health facilities in the northern half of Gaza, the Indonesian Hospital has largely ceased operations but is still sheltering patients, staff and displaced residents.
Israel has ordered the evacuation of the north but thousands of civilians remain.
Food, fuel, medicines and water have been running out across the enclave under Israel's six-week-old siege.
Medical charity Medecins Sans Frontieres said its clinic in Gaza City also came under fire on Monday.
In the south, where hundreds of thousands of Gazans who fled the north of the enclave are sheltering, at least 14 Palestinians were killed in two Israeli strikes on houses in Rafah, according to Gaza health authorities.
At least five people were killed and 10 wounded when an Israeli air strike hit an apartment unit in Khan Younis, at the southern end of the strip, according to medical sources at Gaza's Nasser Hospital.
There was no immediate Israeli comment.
Hamas says it has launched a barrage of missiles towards Tel Aviv and other parts of Israel.
Hamas meanwhile said on its Telegram account that it had launched a barrage of missiles towards Tel Aviv.
Witnesses also reported rockets being fired at central Israel.
Despite continued fighting, US and Israeli officials said a Qatari-mediated deal was edging closer to free some hostages.
US President Joe Biden said he believed a deal was near.
