The Israeli army said it did not realize the car's passengers were journalists and only attacked because the vehicle was driving in a suspicious manner near Israeli troops in the middle of a combat zone.
Two Hamas militants were killed in separate airstrikes, officials said.
The airstrike on the journalists' car came as Israeli soldiers backed by two dozen tanks, two bulldozers, helicopters and drone planes moved into an area just inside the Gaza Strip near the Karni crossing, witnesses and Palestinian security officials said.
The army said the troops were searching for explosives planted by Palestinian militants alongside the border fence and for tunnels under the border. After the operation began, groups of militants repeatedly gathered to try to attack the soldiers, the army and witnesses said.
The Reuters cameraman, Fadel Shama'a, 23, and Sabah Hamida, 25, who worked for a local television company, had the doors open and were about to get out of the armored vehicle in the nearby Shajaiyeh neighborhood to film the raid when it was struck by the missiles, according to Shamas Odeh, chief of Reuters TV in Gaza.
The cameramen, along with three bystanders, were injured with shrapnel wounds and all five were to undergo surgery, hospital officials said.
The front seats of the car were covered in blood and shrapnel had ripped up much of the inside of the vehicle. One of the bulletproof windows was completely destroyed.
The white sport utility vehicle was emblazoned with the Reuters logo and had "TV" and "Press" written on it in English, Arabic and Hebrew.
"This is a cold-blooded crime," said Mohammed Dawdi, head of the local journalists union.
Capt. Noa Meir, an army spokeswoman, said the vehicle was the only one in the combat area, was driving suspiciously and came near Israeli forces during the nighttime raid.
"That's why it was targeted. It was seen as a threat," she said. "There were no clear TV marks (on the car). At least we didn't see one."
"It's unfortunate when journalists get hurt, but that is not the intention," Meir added.
However, the area was an active battlefield and the reporters should not have been there, she said, adding that three Hamas militants attacked soldiers from the same spot 10 minutes after the airstrike.