Egyptian security sources said Youssef Tahan, 60, was a diabetic and fell into a coma before being taken to hospital, where he died on Wednesday. They did not give details of the reason for the coma.
An Israeli official in Cairo confirmed Tahan died soon after reaching hospital, adding, "The embassy is taking care of transferring his body back to Israel."
The security sources said Tahan was arrested in 1985 for smuggling drugs into Egypt and was sentenced to death the following year.
Egyptian officials say the country is facing a growing problem with drugs smuggled from abroad. They say heroin is smuggled in mainly from Israel and Lebanon.
Drugs in Egypt are used mostly by richer people because of their high prices, but the trade causes crime as poorer addicts steal to fuel their habits.