Not Danish or Polish but German. It appears to be Sorbian, i.e., originating among the Slavic speakers of Eastern Germany. It looks like one of several versions of the same name, others being Miedeck and Mietheck. There is a discussion in German of Miedecke here -http://www.onomastik.com/forum/post-4508.html
Three or four possible meanings are mentioned, but the respondent favours a version of the Sorbian given name Mjeto, explained as "Martin".
I notice the similarity of Mietheck to the Polish Mietek, which is a diminutive of an old Slavic name, Mieczyslaw.