The Israeli army said on Monday its troops treated a wounded Israeli civilian brought by a vehicle to a checkpoint near the Egyptian border and then transferred him to a hospital.
An Egyptian official said in Cairo that security forces had shot at someone suspected of trying to cross the border illegally with smuggled goods.
The official could not say whether anyone had been wounded but said that the shooting was under investigation.
Israeli media said the man was evacuated by helicopter and listed in moderate condition with a back injury.
The incident along the normally quiet border occurred about 60km south of a frontier where Egypt posted border troops to prevent Palestinians from smuggling arms after Israel withdrew from the Gaza last month.
A military source said the Israeli appeared to have been shot from inside Egypt but that the circumstances were unclear.
Israel took the two Israelis travelling with the wounded man in for questioning, the source said.
Egypt in 1979 was the first of two Arab countries to sign a peace treaty with Israel. Border incidents have been extremely rare since.
Jordan also signed a peace treaty with Israel, in 1994.