Go to Settings/Audio and turn the Music slider down to something bearable. Of course, this lowers the volume of all music. I set it at about 10, which you can still hear a little, but in combat you can't hear at all.
I really hate when the tinny, uninspiring combat music ruins my enjoyment of the beautiful zone melodies, so I too wish there were a way to turn off specifically combat music.
If the combat music actually worked with the zone music I wouldn't mind it, but the combat music in ESO can be summed up as a bunch of people chanting some random lyrics as a child bangs a couple of pans together while the trumpet player goes out of his way to make loud noises.
It tries so hard to sound epic, but it just sounds obnoxious.
If you are on PC there is an add-on for it. I tried it the others day though and for me it just disabled all music. Maybe it's because it's outdated. I didn't see any settings for it either.