When one says that a button is undone, it is almost always understood that it is by accident that one of the buttons on a garment isn't buttoned. When a button gets unbuttoned by accident, you can say that, for example, Your top button has come undone, or My button came undone and everyone could see and they laughed at me.
If you order someone to button a button that has come undone, you can tell them Fix your button. I can only find one instance where do is used to mean "button." It is in a Parenting magazine in an article advising young parents on how to teach their children to groom themselves. If the child insists that the mother button his shirt for him, the mother is advised to tell the boy Now I'll do a button, then you do a button. Basically, do your button would probably only be appropriate to say in some kind of joint attention scenario where buttons are of high salience, and where buttoning a button is a kind of effortful activity.
For a non-native speaker, stick with fix your button or button your button.