Of course you must define Music Teacher. If you want to teach Music, Band, Choir, Orchestra, or anything in a public school (in Canada or U.S.anyway), you need a bachelors degree and state (province) teacher certificate. Some states (NY for sure) require a Masters degree within 5 years of being hired.

If you want to hang out a shingle to teach anything privately, you need nothing.

I would imagine extensive professional performance experience would be a requirement to teach at a university. I would imagine some in those positions have neither a degree nor a teaching cert.