"An Israeli soldier... was killed earlier this morning," an army statement said.
"A terrorist who was identified infiltrating Israel from the southern Gaza Strip opened fire at Israeli soldiers, who responded with fire. During the exchange of fire, the terrorist was killed," it said.
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Military sources said that in response, aircraft and tanks fired warning shots into the Gaza Strip.
According to Israeli media, the incident took place near the Kissufim crossing.
The Israeli military maintains an exclusion zone just inside the Gaza border that is off-limits to Palestinians, and troops regularly carry out military activity in the area.
Last week, an Israeli army officer and a soldier were wounded in an exchange of fire with Palestinian militants across the Gaza border.
