Militants attacked the senior military commander convoy while he was checking Shaykh Zuwayed area near the border with the Gaza Strip.
One girl was hurt during the exchange of fire and died later in hospital, the army said. Militants who were in a truck were chased down and stopped.
"There have been several attacks in Sinai on army and police officers to create chaos in the area and harming the stability and national security of Egypt," the army said.
Sinai is known to be a stronghold of hardline Islamists and trouble has started in Sinai concurrent with the ousting of President Mohamad Morsi.
Leading Muslim Brotherhood leader Mohamed al Beltagy said that violence in Sanai will stop as soon as Morsi is reinstated as Egypt's president.