German Interior Minister Thomas de Maiziere, who is part of Angela Merkel's Christian Democrats Union (CDU), said he was open to the idea while speaking on a campaign trail last week.
Although he said many of Germany's public holidays are Christian, and it should stay that way, he added: "In places where there are many Muslims, why can't we think about introducing a Muslim public holiday?"
However, other politicians have voiced their opposition to the idea.
Senior CDU member Wolfgang Bosbach told newspaper Bild that people can celebrate whatever religious holiday they want, but "whether the state should also protect non-Christian holidays with legal regulation in future is a different issue entirely."
Also, Alexander Dobrindt, a senior figure in the Christian Social Union (CSU), the Bavarian version of CDU, told Bild that Germany's Christian heritage was non-negotiable.
A spokeswoman for the Interior Ministry said de Maiziere still believed Germany's public holidays were of a Christian nature "and don't have any other roots".
She added that he doesn't have any influence on whether there should be public Muslim holidays or not because according to German law, individual states have to decide.
She also said Hamburg and Bremen have signed agreements with Muslim organisations so that Muslim students could have time off school, and workers could take time off work for holidays important to Islam.
