Yehuda Weinstein said that even though Habtom Zarhum, 29, was an illegal immigrant, his family was entitled to compensation, as he was "a victim of terrorist acts".
Weinstein did not specify how much would be paid.
Zarhum was killed on October 18 at a bus station in the southern city of Beersheba after being mistaken for an assailant in an attack that killed the soldier.
Footage of him bleeding as an angry crowd rained blows on him spread rapidly on social media, prompting soul searching among Israelis over their response to a wave of attacks as well as their treatment of African migrants.
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Four Israelis were arrested over the attack, and are expected to be charged soon.
Zarhum's autopsy ruled he died of gunshot wounds, rather than the vicious beating he received as police officers looked on.
His death came in the middle of a surge of violence that has killed nine Israelis.
Many attackers and suspected assailants have been shot dead.
A total of 62 Palestinians and one Israeli Arab have been killed in the violence, among them those who were shot in clashes with security forces.