At the Awja crossing point in central Sinai on Thursday the Israelis handed over to the Egyptian authorities the body of the man, named as Ayesh Suleiman Moussa, 32, they added.
The Israeli-Egyptian border is a busy conduit for smugglers and migrants seeking work in Israel, mainly Africans.
Egyptian border guards have often shot and wounded or killed African migrants but it is much less common for Israeli forces to shoot Egyptian Bedouin, the nomads indigenous to the desert peninsula.
An Israeli official told Ynet In February that an unusual number of 1,000 African refugees had infiltrated Israel in the two previous weeks.
According to police and IDF estimates, some 10,000 people have entered Israel from Africa over the past five years through the Egyptian border. The breached border has made the infiltration very simple.
Tani Goldstein contributed to this report