Israel Defense Forces soldiers shot and killed an armed infiltrator from Egypt in the early hours of Wednesday morning, the army said.
A military spokesman said troops identified a group of armed men attempting to cross the border near the southern Israeli city of Eilat.
The soldiers opened fire, killing one of the men, the army said. The other members of the group fled, leaving behind them a package which the army later said contained drugs.
Later Wednesday, Egyptian security officials said they found the body of an Egyptian smuggler in the area of the shooting. They said there were two bullet wounds to the man's back but did not confirm it was the same person that Israeli troops shot.
The incident took place on Tuesday along a desert border where attempted penetrations, usually by smugglers or migrants seeking jobs, are common.
Israeli forces cooperated with the Egyptian army in the operation, the IDF said.
In April, Egyptian border guards and seriously wounded an Ethiopian migrant trying to cross illegally into Israel, and arrested seven others, police said.
Egypt has been under mounting international pressure to both secure its border with Israel and to stop using lethal force to stop migrants from crossing the border illegally.
Navi Pillay, the United Nation's top human rights official, in April sharply criticized Egypt for using lethal force to stop migrants from crossing illegally into Israel.
Pillay said she knew of "no other country where so many unarmed migrants and asylum seekers appear to have been deliberately killed"