The tent near the Karmei Tzur settlement in the south of the occupied Palestinian territory burned on Saturday, causing no injuries but leaving Jewish religious books damaged and destroyed, police said.
Israeli media reported that police suspected residents of the nearby Palestinian town of Halhul.
Netanyahu alleged on his Facebook page that the synagogue "was set on fire by Palestinians".
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"We will prosecute the perpetrators of this crime. I expect the international community to condemn the desecration of a synagogue, an act that is the result of incessant Palestinian incitement."
The synagogue was dedicated to Naftali Frenkel, Gilad Shaer and Eyal Yifrach, who were abducted from a hitchhiking stop near the flashpoint West Bank city of Hebron in 2014 and later killed. Their bodies were discovered in the area.
A few weeks after their kidnapping, 16-year-old Palestinian Mohammed Abu Khdeir was abducted and burned alive in a revenge plot by three Israelis.
Two of them -- who were 16 at the time of the killing -- were sentenced on Thursday, with one receiving a life term and the other 21 years.
The incidents were part of a spiral of violence that led up to the 2014 Gaza war.