The other five men were injured while trying to cross the barbed wire border fence and were also admitted to hospital.
Up to 25 migrants have been killed this year by Egyptian police along the 250km-long border with Israel.
African migrants in Egypt complain of poor treatment and discrimination, and hundreds have been arrested while trying to slip into Israel.
The border has become a major transit route for migrants, asylum-seekers and drug smugglers, prompting Israel to ask Cairo's help in clamping down on the traffic.
In August, Amnesty International urged the Egyptian government to launch an investigation into the use of lethal force against illegal migrants.