The Israeli military said it opened fire on crowds who breached the security barrier separating Israel and the Palestinian territories and approached an army post.
Tensions between Israelis and Palestinians on the Gaza border have been mounting since late March, which marked the start of a wave of protests called the "Great March of Return".
Two other Palestinians were killed in other protest locations, the ministry said, adding that at least 140 Palestinians were wounded by live bullets. The Bedouin village is said to be slated for demolition and Palestinian villagers have been protesting against the imminent move.
Israeli army spokesman Jonathan Conricus said around 20 Palestinians had crossed the border in an "organised attack" after an explosive device destroyed a portion of the fence.
But thousands of protestors again gathered Friday in sites along the border, AFP correspondents said.
Top Palestinian official and member of Fatah, Ahmad Majdalani, said the party remains suspicious of the Qatari role in meddling in the affairs of the Gaza Strip, controlled by Hamas.
A group of Israeli paramilitary settlers attacked a Palestinian couple south of Nablus, in the northern part of the West Bank, on Friday, killing the woman and severely injuring her husband.
After the murder of Israeli activist Ari Fuld who was stabbed in the back by a Palestinian terrorist two weeks ago there has been a significant uptick in terrorist activity in Judea and Samaria.
Israel accuses Hamas of orchestrating the weekly border riots that have taken place since March to provide cover for attacks.
One day after vowing to "reach an understanding that will bring calm to Israel", Hamas leader Ismail Haniyeh did an about-face, cheering for the continued violence on Gaza's border.
The Palestinian leadership has rejected any future cooperation with United Nations special coordinator for Middle East peace Nickolay Mladenov, informing the worldwide body that he is "no longer acceptable" because he has "gone beyond his role" in attempting to broker agreements between Israel and Hamas.