"The country will not tolerate this new injury which goes against the values that all French people share," said Bernard 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 purposes, were knocked over while in 2001, 54 tombs were wrecked.
It comes as France's more than half a million-strong Jewish community is feeling increasingly vulnerable after last month's deadly attacks in Paris, and amid a steady rise in already high levels of anti-Semitism.
numbers of French Jews are already emigrating - particularly to Israel - due to anti-Semitism compounded by a weak economy, but of four Jewish shoppers in a Paris supermarket in January has caused even more to consider to move.
Following the deadly attack France's Prime Minister Valls said that an exodus of Jews from the country would mark "the failure of the French republic."