The Security and Intelligence Service, or PET, said the men were arrested at two separate sites in the Danish capital in connection with an ongoing terror investigation.
Aside from facing preliminary charges of possessing illegal firearms, PET said they are "suspected of having been in the process of preparing a terrorist act." The agency did not give any details about the target.
"The investigation will establish whether possible terror threats have been addressed and averted by the arrests," the agency said in a statement.
Preliminary charges are a step short of formal charges.
PET described the men as a 22-year-old citizen of Jordan, a 23-year-old Turkish man living in Denmark and a 21-year-old Danish national who lives in Egypt.
The men face a custody hearing on Saturday, Copenhagen police spokesman Svend Foldager said. Such hearings in Denmark are often closed sessions in terror cases.
PET would not say if it suspects the men belong to a specific terror network. Since the 2005 publication of 12 caricatures of Prophet Mohammad in the Jyllands-Posten newspaper, however, the agency has repeatedly warned that Denmark would be the target of radical Islamist groups.
The prophet cartoons triggered riots in many Muslim countries, and militant Islamists called on followers to avenge them. Islamic law generally opposes any depiction of the prophet, even favorable ones, for fear it could lead to idolatry.
Four Swedish residents are already on trial in Denmark for plotting a shooting spree in December 2010 against Jyllands-Posten's Copenhagen office.
In May, Chechen-born Lors Doukayev was sentenced to 12 years in prison for preparing a letter bomb that exploded in a Copenhagen hotel in 2010. Doukayev, a 25-year-old resident of Belgium, was wounded when assembling the device, which is believed to have also been intended for the Jyllands-Posten. No one else was injured.