The court in Glostrup, near Copenhagen, remanded the three in custody for four weeks after a closed-door hearing.
"The court has complied with the prosecution's request for custody for four weeks, the first two weeks in isolation," Lykke Sørensen, the head of the legal department of Danish intelligence agency told TV2.
The trio was arrested Wednesday along with two other men for hatching what Danish officials called a plan to "kill as many people as possible" in an imminent assault on the Copenhagen offices of the Jyllands-Posten daily.
In 2005, Jyllands-Posten published a dozen cartoons of the Prophet Mohammed that triggered violent and sometimes deadly protests around the world.
Denmark's intelligence service, PET, only identified the three men remanded in custody as a 44-year-old Tunisian, a 29-year-old Swede born in Lebanon, and a 30-year-old Swede.
It said all three resided in Sweden and drove to the Copenhagen suburbs overnight Tuesday.
The Swedish tabloid Expressen, named the suspects as 29-year-old Munir Awad, 30-year-old Omar Abdalla Aboelazm, and 44-year-old Tunisian national Mounir Dhahri.
According to the paper, Awad had been arrested twice before on suspicion of links to terrorism: in 2007 in Somalia and in 2009 in Pakistan along with Mehdi Ghezali, a Swede who had spent two years in Guantanamo Bay.
Danish intelligence said Wednesday the men would face charges of "attempted terrorism."
The head of the intelligence agency said some of the suspects were part of "a militant Islamic group with links to international terrorist networks."
A fourth man arrested Wednesday in Stockholm in connection with the plot was set to appear in court in the suburb of Sollentuna at 3pm.
Official documents showed the court would decide if the suspect -- 37-year-old Swedish citizen Sahbi Zalouti, who according to PET is of Tunisian origin -- would be remanded in custody for "preparation of terrorist crimes."
A PET spokeswoman said the fifth man detained Wednesday -- a 26-year-old Iraqi asylum seeker arrested in his apartment in a Copenhagen suburb -- would be released.
"He is still suspected of trying to conduct terrorism," Trine Marie Ilsøe told AFP, adding he could not be remanded in custody since he had not been sent before a judge.
She did not specify why he had not gone to court with the three others, but Danish media reported the suspicions against him were not as serious as against his suspected accomplices.
PET said officers also seized "plastic strips that could have been used as handcuffs, a sub-machine gun with silencer as well as ammunition," during the arrest operation.
Danish Prime Minister Lars Løkke Rasmussen on Wednesday said "there are extremists out there who want to attack our open society."
Wednesday's arrests took place after an extended joint investigation with Swedish intelligence agency Säpo, which had the men under surveillance for several months.
Police evacuated the building where the 26-year-old Iraqi lived for several hours overnight Wednesday after discovering a suspicious object there, media reported.
A bomb-disposal robot was sent in and ambulances and fire engines were on stand-by, but it turned out to be a false alarm.