An Egyptian security official said the Israeli had no identification papers or money but told his investigators he was reporting on African migrants sneaking into Israel from Egypt.
The Haaretz newspaper identified the man as Yotam Feldman. It was not clear whether he was working on assignment for the paper when he was captured.
The Israeli military said it was trying to secure the man's release.
A medical official in the Egyptian city of Rafah said the 30-year-old Israeli hurt his hand on the barbed wire fence as he tried to cross the border.
Both officials spoke on condition of anonymity because they were not authorized to discuss the arrest.
Smugglers help hundreds of African migrants to cross into Israel every year from Egypt seeking work.
Over the past few years, the number of illegal migrants has spiked. Most come from Sudan and the horn of Africa, and often attempt night crossings with the help of Bedouin smugglers.
The United Nations and other international agencies have criticized Egypt for shooting at some of the migrants as they attempt to breach the border into Israel. Around 40 have been shot dead trying to cross the border.
Israel, worried by the mounting influx of refugees, announced in January that it would build two walls along the border with Egypt to stem the flow.
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