Repeating a move by conservative Danish paper Jyllands-Posten last September, Magazinet published the controversial drawings in the name of "freedom of expression" on Tuesday.
The same caricatures have been blasted by Muslims in Denmark and abroad, since images of the prophet are considered blasphemous under Islam.
"Just like Jyllands-Posten, I have become sick of the ongoing hidden erosion of the freedom of expression," Magazinet editor Vebjoern Selbekk wrote.
The murder of Dutch filmmaker Theo van Gogh in 2004 revealed "that we are not facing empty threats. We know that the freedom of expression in our part of the world is being threatened by religion that is not afraid of using violence", he added.
The editor said he was not afraid of the prospect of facing the same indignation and even death threats that faced the Danish paper after it published the cartoons.
Meanwhile, Denmark's prime minister on Tuesday accused a group of local Muslims of smearing the country's reputation in the Middle East as they sought support against a newspaper that published caricatures of Islam's Prophet Muhammad.
Anders Fogh Rasmussen said he was "stunned" that leaders of the Islamic Faith Community had travelled to Egypt, Syria and Lebanon "to stir up attitudes against Denmark and Danes".
The group's leader, Ahmed Abu Laban, a cleric, has defended the December trip, saying the Muslim community was feeling marginalised in Denmark in its protests against the paper.
Muslim leaders in Denmark and abroad have condemned the drawings, one of which shows Muhammad wearing a turban shaped as a bomb with a burning fuse.
Islamic tradition bars any depiction of the prophet, even respectful ones, out of concern that such images could lead to idolatry.
"Just like Jyllands-Posten [Danish newspaper], I have become sick of the ongoing hidden erosion of the freedom of expression"
Danish Muslims groups have called on authorities to prosecute Jyllands-Posten, but a regional prosecutor said last week he would not file charges.
On Tuesday, the prime minister directed his criticism towards the Muslim group, saying "misinformation" about Denmark had appeared in the Arab media after their tour of the Middle East.
Kasem Ahmad, a spokesman for the Islamic Faith Community, denied the group had spread false information about Denmark.
"The Islamic Faith Community has not said anything wrong," he said. "We did nothing wrong by seeking help abroad and making use of our freedom of speech."