It is the eighth African shot at the border this month.
Security and hospital officials say the men were illegal migrants trying to cross into Israel near the Egyptian border town of Rafah on Tuesday.
They say the Africans ignored warning shots.
Three Ethiopians traveling with them told police they had paid Bedouin traffickers $1,000 each to cross the border.
The officials spoke on condition of anonymity because they were not authorized to speak to the media.
Hundreds of Africans seeking jobs try to reach Israel every year.
Egypt has killed dozens of migrants at the border, drawing criticism from rights groups.