I think you could use Rename, Move & Copy, under Library Tools, to move them according to Genre. But why bother? MC will separate them, no matter where they are physically located.
Before making a start on ripping CDs back in 2013, I made a detailed study of my options for file and folder naming. I was well aware that metadata was the key that enabled easy browsing of my (95% classical) collection using software such as JRiver Media Center on my PC and MinimServer on my NAS, but I still wanted wanted the physical folder structure to make sense - especially as I was planning to store MP3 copies of my music files on my Android phone (using the same folder structure), for use when I was away from home and without a reliable connection to my NAS.
At that time, I couldn't find any Android music player app that understood the special needs of classical music (focused on Composer and Work, rather than Artist and Album). Even today, I don't think there are any Android music players that meet my needs for classical metadata-based browsing. I therefore wanted the physical location of the music files on my phone to be easily browseable.
To achieve this, I decided to store most of my classical rips in a folder hierarchy of Composer, Album, and Work, with most of my non-classical rips being stored in a simpler hierarchy of Artist and Album. Compilation albums are handled in a slightly different manner. It didn't take too much effort to configure dBpoweramp CD Ripper to do all this automatically (helped by the fact that it has a Compilation checkbox).
Sadly, it doesn't look like MC can do the same thing. Manually moving the files after an MC rip using Rename, Move & Copy would be a tedious process that would more than negate the benefits of avoiding the manual import of a dBpoweramp rip.