Tawfiq Abu Riala, 34, was killed and two other Gaza fishermen were arrested, said Ashraf al-Kidra, a Gaza health ministry spokesman.
The two other fishermen were arrested and taken to Israel, spokesman Ashraf al-Qudra said.
An Israeli army spokeswoman said four Palestinian boats had strayed out of their designated fishing zone overnight Friday.
"Soldiers fired warning shots then targeted the engines of two of the boats, which were then transferred to Israel for investigation," she said. "The two other boats were able to return to Gaza."
The spokeswoman added that the Israeli navy was on alert "to prevent arms transfers into the Gaza Strip" but did not comment on casualties.
Following last summer's 50-day war in Gaza, Israel agreed to double the permitted fishing zone for Gazans to six nautical miles. It recently also loosened restrictions to allow Gaza fishermen to export their catch to the West Bank for the first time since 2007.
Around 4,000 fishermen work in Gaza, more than half of whom live below the poverty line.