"Soon Denmark will be hit by the terrorist attacks that will make what happened on February 14 look like pranks," Denmark's TV2 quoted the leaflet as saying.
The attacks cited in the leaflet claimed the lives of two civilians at a free speech debate and a synagogue.
One of the fliers warning of another attack was found on the wall of the cafe that hosted the free speech debate two months ago. Another was found near a memorial honoring a 55-year-old filmmaker killed during the debate.
"Some notes have been found hanging in Copenhagen. I cannot comment on the content, but we are investigating it," Carsten Reenberg, Copenhagen Police security chief, was quoted as saying.
The suspected gunman that carried out the two terrorist attacks on February 14, Omar El-Hussein, was killed by police the following day. Local authorities say the perpetrator had a criminal record and was released from prison two weeks ahead of the attack. Although he was not part of a terror cell, El-Hussein was believed to be inspired by a string of deadly terrorist attacks that took place in Paris, France a month prior.