“The country will not tolerate this new injury which goes against the values that all French people share,” said Bernard Cazeneuve without giving further details of the incident in the town of Sarre-Union.
“Every effort will be made to identify, question and bring to justice the person or persons responsible for this ignominious act,” he added.
French Prime Minister Manuel Valls, writing on Twitter, also condemned the desecration, calling it “an anti-Semitic and ignoble act.”
It is not the first time that a Jewish cemetery in Sarre-Union has been targeted.
In 1988, around 60 Jewish steles, stone or wooden slabs often used for commemorative purposes, were knocked over while in 2001, 54 tombs were wrecked.
News of the latest incident comes just over a month after an Islamist gunman shot dead four Jews in a supermarket siege in Paris.