According to the Arutz Sheva media network, the JIJ accuses Haniyeh of two grave crimes – recruiting children to take part in military operations and terror attacks and also using them as human shields.
Such activities have reportedly affected some 17,000 children since 2016.
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JIJ Attorney Uri Morad expressed hope for the impartial and fair probe.
"The entire process was very efficient and organized, and we felt like we had the trust of those receiving the request. I believe that this suit, which the Jerusalem Institute for Justice has submitted, will be dealt with fairly and without bias," Morad said, as quoted by Arutz Sheva.
Hamas is accused by Israel of escalating tensions in Gaza, which the movement governs, by sparking violence and provoking Palestinians to penetrate the security border.