Mazen Abu Odeh, 21, was killed when a tank shell hit his house in Beit Hanoun, witnesses and medical officials said. One of the two wounded was in a serious condition.
Odeh's father, brother and sister were killed by Israeli fire during an incursion into Beit Hanoun two months ago.
An Israeli army spokesman said that there was "no tank shooting in that area" but said that it had carried out an air raid "in the same area on a rocket launcher that had been used to fire in the direction of Israeli territory".
Israel re-entered the Gaza Strip in June, after Hamas fighters carried out a cross-border raid, killing two soldiers and capturing a third.