The person had attempted to source firearms and ammunition to carry out one or more terrorist acts in an undisclosed place, Jorgen Bergen Skov, chief inspector of the Copenhagen police, told a news briefing.
The suspect, who was charged with a terrorist offence, appeared to have been inspired by Islamist militants, Skov said, and will be put before a judge for preliminary questioning on Friday.
The police worked together with security and intelligence officers to carry out the arrest.
"This unfortunately confirms a serious terror threat in Denmark," Flemming Drejer, chief inspector of the Danish intelligence service, told the briefing.