Dr Muawiya Hassanein, the head of Gaza emergency services, and officials at the Nasser Hospital in Khan Yunis identified the man as Hossam al-Najar, 40, without specifying whether he was a militant or a civilian.
Three fighters from the armed wing of the Hamas movement were wounded in a separate air strike and a fourth man suffered a gunshot wound as he stood outside his home, Hassanein said.
The fighting erupted after Israeli tanks backed by helicopters pushed about one kilometre (some half a mile) into the Hamas-controlled territory east of the southern town of Khan Yunis, witnesses said.
An Israeli military spokeswoman said the army was carrying out an operation against "terror infrastructure" in the area and had launched an "aerial attack againt a gunman approaching the forces."
Israel launches near-daily raids on the territory, which has been ruled by the Islamist Hamas movement since June, in an effort to halt persistent rocket and mortar attacks on Israeli communities near the border.