The woman, who was Eritrean, had ignored orders to stop and was shot in the stomach and leg, officials said.
At least three other people, all Eritrean, were detained, including a child aged four.
Human rights activists have criticised Egyptian soldiers for killing dozens of African migrants at the border in the past two years.
The woman, 38, was shot close to the Egypt-Israeli border in central Sinai.
The death brings to 19 the number of African migrants killed this year while attempting the crossing into Israel, according to the AFP news agency.
At least 17 migrants were killed at the Egypt-Israel border in 2009. Egyptian police claim they are trying to control people-trafficking.