I'm currently working in a project that is funded by me and the supervisor doesn't contribute much to my work (he is just directing me slightly if I asked him) and he told me that he doesn't need to publish and I can publish as a sole author if I want. I only have a Master degree, can I publish as a sole author? can some journals accept that? Should I contact a journal to ask? if the journal agrees, so this is will be fine? (By the way my field is Biochemistry)
Everyone can submit articles to journals, there is no degree requirement. There is nothing negative about single author manuscripts.
Manuscripts should (ideally) be evaluated by its content not by its author list.
I am a PhD student in Aerospace engineering and my research is computational mechanics. The first 4 papers of mine are publicized all by myself (IF: 1.9-2.8). It's simply because the work is done only by me and I am a self-motivated researcher. Now, I also have papers with my advisor. You need to talk with your advisor and ask his opinion. My advisor just told me that since he did not contribute to the work, he did need to list his name on my paper. I believe this is the answer for most professors.
However, I have to admit that most grad students' first paper is publicized with their advisors. That is the main reason that you have this question. But journals never care about it. When I publicized my first paper, the journal editor called me prof. Li. At that time, I was just a MS student.