I had an empty standard installation of MySQL but somehow I could not create a database using the InnoDB engine. The engine was just not activated (you can check that with the
command). If it states support: no it is inactive or not available. As I was sure that InnoDB is supported using the default installation of the official Debian Package I did some research on the internet. I found out that InnoDB is automatically disabled if something is bad with it’s data files. You can just remove all files that start with "ib" from the directory /var/lib/mysql. After a restart of the service everything worked fine.