Retired Art Teacher
The terminal degree for teaching art in college or university is a master of fine arts (MFA). This would be after a 4 year college degree, such as a bachelor or arts (BA) or a bachelor of fine arts (BFA). In addition, most colleges and universities expect their art professors to be practicing artists and to show their work in galleries on a family regular basis.
If you are thinking of teaching art at the high school, middle or elementary school level, then in addition to art classes, you will need classes in art education and general education. Requirements vary by state and school district, but usually a BA with a major in art, or a BA with a major in art education is the basic degree to have. Some school districts require a masters degree, such as were I taught, so I had an undergraduate degree in art history (BA) and I got a master of science in art education (MS).
You can find out more about teaching art at the National Art Education Association website, www.NAEA.org