"After the strike, a terror cell fired with machine guns at an (Israeli) aircraft, without actually harming it".
It named him as Abdullah al-Shahari, 28, and said the shooting took place east of the southern Gaza town of Khan Yunis.
It said the bomb was planted at the frontier under cover of mass Gaza protests in the area.
Meanwhile, Gazans are preparing for a third consecutive Friday of protests along its border with Israel.
Israel has drawn sharp criticism for its open-fire orders along the border, including its warnings that those approaching or trying to damage the fence would be targeted.
The White House has called on Palestinians to engage in exclusively peaceful protests and stay at least 500 meters from Gaza's border with Israel, on the eve of fresh demonstrations along the border. That day will mark the 70th anniversary of Israel's establishment - an event Palestinians refer to as the "Nakba" or "Catastrophe".
Mohammed Hijaila was killed and another man seriously wounded early this morning during the strike, the health ministry in the Hamas-controlled enclave said, confirming he was a member of the movement's militant wing.
The Gaza security fence has been the site of a serious uptick in tensions between Israel and Hamas.
The same source also displayed that the bombing was carried out in response to an explosive charge that on Wednesday detonated without provoking casualties east of Shujaiyeh, near the Gaza border, in the vicinity of an Army military engineering team.