The incident was reported on Saturday.
"Our Jewish citizens must be respected and not live in fear," she added, according to TheLocak.dk website.
A police spokesman said: “There are no symbols or words written on the gravestones but paint has been daubed on them.”
It was one of a number of antisemitic incidents in Denmark last weekend, the anniversary of Kristallnacht.
Local reports said a Star of David had been pained onto the letterbox of a family in Silkeborg, on the Danish mainland peninsula of Jutland.
The cemetery at Randers dates back to the early 19th century when the town was home to around 200 Jews.
Around 6,000 Jewish people live in Denmark today, most of them in Copenhagen.
