Officials added it was their view that the motive of the attack had been to target “a particular population group on the basis of their religion”, and told Danish broadcaster DR that they were still appealing for witnesses.
The arrested men were due to appear in court on Wednesday afternoon.
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, a nearby city in Jutland.
Danish Prime Minister Mette Frederiksen said the graveyard incident was “both an attack against Danish Jews and against all of us”.
“Our Jewish citizens must be respected and not live in fear,” she added, according to TheLocak.dk website.
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.
