Police raided 11 homes in the early hours of Tuesday.
Television footage shot from a helicopter showed bomb squads and forensics officers at some of the locations.
"We made our move now because we had gathered enough evidence to make an arrest, and because several of the suspects had created an unstable explosive in a densely populated housing area," he said.
"During the raids overnight and this morning we found a series of objects and materials that are important in this case," he added.
Six of the eight suspects were Danish citizens and the had foreign backgrounds from Afghanistan, Pakistan, Somalia and Turkey, and six of the eight held Danish citizenship, Scharf said.
"This is a serious case. A case which we have been investigating very intensively... A case which has required much of PET's resources, a case which has had high priority for us," he added.
This is the third time in two years that Danish police have arrested people it suspects of preparing acts of terrorism.
In September 2006, PET arrested nine people after finding chemicals used in explosives production during a raid. Four young Muslims were indicted and accused of planning attacks in Denmark or abroad. Their trial is to begin on Wednesday.
Denmark has not been targeted by a terrorist attack for more than two decades.