The men are suspected of vandalism and could also face charges under anti-racism laws.
A police prosecutor is expected to requested Randers District Court remand the men in custody on Wednesday afternoon, police said in a press statement.
The men are from the central Jutland towns of Randers and Hobro.
Police suspicions against the men are related primarily to vandalism at Østre Kirkegård cemetery in Randers during the night between Friday and Saturday last week. 84 gravestones were defaced with green paint.
Vandalism at a building in the town, where green and black paint was thrown at the façade, is also encompassed by the case.
Police are still looking for further witnesses who may be able to assist with investigation.
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In addition to the Randers incidents, anitsemitic vandalism was also reported last weekend in Copenhagen, Aarhus, Silkeborg and Aalborg.
In Norway, several yellow Stars of David were placed outside the printing offices of publisher Schibsted in Bergen.
Neo-Nazi group the Nordic Resistance Movement (NRM) has been linked to the vandalism in Denmark, but has denied carrying it out.
The incidents occurred around the 81st anniversary of the 1938 Kristallnacht anti-Jewish attacks in Nazi Germany.
A report has been filed with Denmark’s police security service PET, police have confirmed.