“More than 80 gravestones were daubed with green graffiti and some were overturned” at the Østre Kirkegard cemetery, according to a police statement.
“There are no symbols or words written on the gravestones but paint has been daubed on them,” news agency Ritzau quoted police spokesman Bo Christensen as saying.
Police said a complaint had been made Saturday.
“The attacks at the weekend… are both an attack against Danish Jews and against all of us,” Prime Minister Mette Frederiksen said in a Facebook message.
“Our Jewish citizens must be respected and not live in fear,” she added.
Many other antisemitic attacks were carried out in Denmark over the weekend, according to members of the Jewish community, including a Star of David painted onto the letter box of a family in the western town of Silkeborg.
The vandalism happened on the anniversary of the 1938 Kristallnacht anti-Jewish attacks in Nazi Germany, a fact that one Jewish community leader said was “proof that the state of mind which led to the Holocaust exists in 2019”.
The Randers burial ground dates back to the early 19th century when the town's 200-strong Jewish community was Denmark's largest outside the capital Copenhagen, which is today home to most of the country's 6,000 Jews.
Copenhagen's Great Synagogue was targeted in a 2015 shooting which saw one security officer killed after an earlier attack on a conference on freedom of expression also left one person dead.
Five police were injured in the twin attacks which saw police gun down 22-year-old perpetrator Omar El-Hussein, a Danish citizen of Palestinian origin.
Both 2017 and 2018 saw 45 antisemitic attacks registered throughout the country.