The attacks began around midday and lasted for about three hours. About a dozen people have been wounded.
The Israeli military says assailants carried out three consecutive attacks near the Egyptian border. The attacks targeted a passenger bus, a private car and a group of soldiers.
Israeli security forces tracked down some of the assailants and exchanged fire with them, killing several. There was no word on whether any attackers were captured alive.
Some of the attackers used heavy weapons and explosive devices during the attacks.
Israel almost immediately said the attackers came from the Hamas-ruled Gaza Strip and made their way through Sinai, which borders both Israel and Gaza. That raised the specter of an Israeli military reprisal against the Palestinian territory.
"The incident underscores the weak Egyptian hold on Sinai and the broadening of the activities of terrorists," Israeli Defense Minister Ehud Barak said in a statement. "The real source of the terror is in Gaza and we will act against them with full force and determination."
The Associated Press contributed to this report.