Israel Police received a complaint regarding 35 headstones which were damaged in the northern Israeli city of Nof Hagalil.
According to a police statement, an employee at Nof Hagalil's old cemetery said that he discovered 35 smashed headstones during a routine inspection on Friday.
Some of the headstones were in the "non-Jewish" section of the cemetery, while most were in the Jewish section.
Policemen arriving at the scene gathered evidence and opened an investigation into the incident.
In a Saturday night statement, Israeli Prime Minister Binyamin Netanyahu said: "The desecration of the graves of the World War I heroes in Haifa is an abhorrent crime."
"We owe these soldiers a historical debt for the liberation of the Land of Israel from Ottoman rule. We are doing everything necessary to find those responsible and bring them to justice."