It is possible to teach English without degree in Japan?

Your profile says you are Malaysian so I assume that you already have a Malaysian accent when you speak English? I really don't know for Japan, but I do know that some countries require that English teachers are native English teachers form one of the five English speaking countries: England, USA, Canada, Australia, New Zealand and sometimes including South Africa. However, not all that many people speak English in Japan, especially in the more rural areas outside the big cities, so who knows. Why don't you try writing to some English language schools there and apply for jobs and see what they say. Or else, visit the Japan Embassy in KL and ask there.

Also, I don't blame you for choosing Japan as a place to live and work, it's an amazing country. I also hope to move there one day.