Do I need research experience to be admitted to a highly ranked mathematical physics master's?
Having research experience will certainly help your application to an elite program.  However, it is definitely not a necessity.  Moreover, the graduate faculty at top institutions are used to fielding applications from all over the globe; they should be reasonably familiar with what kind of preparation students from Germany will typically have.

However, if you are serious about pursuing graduate studies, only applying to a small number of top programs is not usually a good approach.  The top programs frequently need to reject a significant number of totally qualified applicants, simply because their space is limited.  I would suggest that you apply more broadly if you want to ensure that you can get into a top program.