An Israeli tank also targeted a Hamas military post during the incident, Israel's military said in a statement.
It said an army officer was moderately wounded and two soldiers were lightly injured by the Palestinian's shooting in the area of the southern Gaza Strip.
There has been tension along the Gaza border since regular protests and clashes erupted there in March 2018.
At least 297 Palestinians have been killed in Gaza or the border area by Israeli fire since then, the majority during demonstrations and clashes.
Seven Israelis have been killed.
The protests have declined in intensity recently after a truce brokered by UN officials and Egypt.
Under the truce Israel agreed to take steps to ease aspects of its blockade on Gaza, which is ruled by Islamist movement Hamas.
Israel and Hamas have fought three wars since 2008.