A separate blast hit a police checkpoint in the Nile Delta in the north of the country. There were no immediate details on that attack.
At about the same time and on the Gaza side of the border, three Palestinian security officers were injured in an exchange of fire with Palestinian militants who tried to ram an explosives-laden car into the main Israel-Gaza crossing, Palestinian security officials said.
The officers opened fire on the car as it approached the Palestinian side of the Karni crossing, the officials said. Unidentified militants in the car returned fire, injuring the three officers. It was not immediately clear what happened to the militants but the car did not explode, witnesses said.
Israel has warned that, since it pulled out of Gaza last summer, Rafa has become a smuggling zone for terrorists and weapons, reports CBS News correspondent Robert Berger.
The attackers hit just two days after a triple bombing that killed 24 at Egypt's Sinai resort city of Dahab on the Gulf of Aqaba.
Wednesday's attack on the multinational base happened just south of the Rafa border crossing to the Gaza Strip and wounded one New Zealander and one Norwegian attached to the multinational force, officials said.
The peacekeeping force was set up as part of the 1979 peace treaty between Israel and Egypt that led to Israel's withdrawal from the Sinai. It is partially paid for by the United States and has U.S. advisers and soldiers attached to it — in addition to soldiers from several other nations, including Canada.
The Sinai — Egypt's desert peninsula that abuts Israel and separates the Mediterranean from the Red Sea — has been wracked by a series of Islamic extremist bombings in the last year and a half.
The multinational force also has a base in southern Sinai.
Egyptian authorities, already struggling with elusive terror cells in the rugged Sinai Peninsula, moved quickly Tuesday — arresting 30 men in the triple bombings that ripped apart a resort town on a tranquil holiday evening.
Radical Muslim groups moved just as rapidly to distance themselves from the Dahab attacks. The leader of Egypt's banned Muslim brotherhood condemned them as "aggression on human souls created by God."
The militant Palestinian Hamas organization called them a "criminal attack which is against all human values."
The targets Monday weren't just Westerners, reports CBS News correspondent David Hawkins, but Egyptians and Egypt's economy.