The death is the third this week and brings the toll of migrants killed at the sensitive border this year to eight. At least 19 migrants were killed by Egyptian border guards last year.
The Sinai border is a main transit route for African migrants and refugees seeking work or asylum in Israel. Egypt has come under pressure from Israel to staunch the flow, while rights groups complain about the methods of the border police.
The man was shot in the back at the border and later died in a hospital in Egyptian Rafah. He identified himself as an Ethiopian but did not carry documentation, medical sources said.
The two injured, a 23-year-old Eritrean and 20-year-old Ethiopian, were transferred to El-Arish hospital.
Analysts and aid workers say the flow of migrants from the Horn of Africa through Egypt to Israel has increased as it has become more difficult to travel on other routes, such as via Libya to Europe. Eritreans make up the largest single group of people trying to cross into Israel from Egypt, though Ethiopians and Sudanese also make the trek.
Amnesty International earlier this month called on Egypt to check their border guards use of excessive force against unarmed migrants, in a week when four migrants were killed.
Security forces say they only fire at migrants after repeated orders to stop are disregarded and that smugglers who ferry migrants to the border sometimes fire on security forces.
