Two others who were arrested at the same time were released, the Danish intelligence service PET said.
Danish Justice Minister Lene Espersen told Danish television TV2 the alleged terrorist case was "the most serious in the country".
Prime Minister Anders Fogh Rasmussen said Denmark needed to "take the terrorist threat seriously" because of its participation in the Iraq war.
Authorities provided no details on the target of the alleged attacks, but said a police raid overnight had uncovered "materials" for the production of explosives.
The sting comes a month after British police uncovered a plot to blow up several US-bound airliners using liquid explosives.
In October 2005, another Danish anti-terrorism operation led to the arrests of seven young Muslims in Copenhagen.
The identity of the new detainees was not revealed, but authorities said they were aged 18 to 33.
Brief court appearance
They were arrested during a police raid overnight in the heavily immigrant-populated neighbourhood of Vollsmose in the town of Odense after a lengthy period of surveillance.
Seven suspects have been remanded in custody by a court in Odense.
They are suspected of plotting one or several bombings in Denmark or abroad, according to police. The remaining two were released.
Ms Espersen told journalists that "most of those arrested were
Danish citizens" of foreign origin though PET said that at least one was an ethnic Dane.
She said she was "concerned that Danes were preparing a terrorist attack in the country."
PET chief Lars Findsen said authorities had decided to "intervene now" because it was "difficult to determine at what stage the preparations were."
"The PET's primary mission is to thwart and prevent terrorist acts, and the (intelligence) service decided it was time to go ahead with these arrests now after receiving information indicating that some people in the group were preparing a terrorist act," Mr Findsen said.
A staunch ally of the United States, Denmark has about 470 troops stationed in Basra, in southern Iraq, under British command.