Palestinian security sources said Tawfik Ali Sharafi, 22, was killed early on Wednesday while four others were wounded in the exchanges of fire with the Israeli army around Jabaliya.
Sharafi belonged to the Izz al-Din al-Qassam Brigades.
Israeli troops had been active around Jabaliya, Beit Lahya and Beit Hanoun in the north of the Gaza Strip since Tuesday evening in a new operation aimed at halting Palestinian rocket attacks on southern Israel.
The gunbattle erupted hours after Israel massed ground troops backed by helicopters and 100 armoured vehicles in its latest raid.
Witnesses said Israeli helicopters opened fire on two strongholds of Palestinian fighters after dark and then sent troops and tanks into the areas of Beit Lahiya and Beit Hanoun.
Sharafi was killed in an ensuing exchange of fire at the eastern edges of Jabaliya.
An Israeli military source said its forces had entered northern Gaza "in an operation to prevent the firing of rockets and mortars against Israeli towns and settlements".
Armed members of the Palestinian resistance had fired four rockets into Israel earlier during the day, but they caused no casualties or damage, the Israeli police said.
Three of the rockets hit the town of Sederot, just across the border from the Gaza Strip.