A Ministry spokesperson said they are aware of the reports and "we are seeking further details."
Posts about the death have appeared online, with one image showing a wreath dedicated to the mother of a deceased person in Gaza who is identified to be a New Zealand citizen.
"The New Zealand Jewish community stands together with you in this difficult time... on the falling of your son," a tribute beside the wreath says.
Another New Zealand born citizen, Adam Agmon was was killed in action in Israel in October.
His brother, Yahel Agmon, said he was killed while performing his duties as a fighter, commander and sergeant in the parachute brigade.
New Zealand Jewish community leader Juliet Moses shared that Agmon had been killed in action after being called to up to fight on Shabbat.
The post said they killed two terrorists in Kibbutz Nirim and Agmon was later killed.
It said he was buried in a regional cemetery in Misigav.
Also noted was that, although Agmon played football in his youth, he loved rugby and the All Blacks, and his family had specifically asked for the news to be shared among rugby fans.
"He was born in New Zealand to Israeli parents and returned at a young age," the post said. "He has already set up with his father to watch together in the World Cup quarter-finals on Saturday against Ireland.
Moses also shared an image of Agmon’s All Blacks tattoo, which his father Oren and brother Yahel also have.
All Blacks fullback Beauden Barrett commented on a Facebook page announcing Agmon’s death.
"Rest in peace Adam. Thinking of his family and friends at this difficult time. Thank you for your support, we will do our best to make him proud," Barrett said.