How can I disable the voicemail button on iPhone? I do not use the voicemail at all and from time to time I keep pressing the voicemail button by mistake. 

I am looking for a solution to this problem. I observed many others are complaining about the same problem, even on Apple's forum but they closed the thread and keep it unresolved :p
I suspect that because the vast majority of people with iPhones do use voicemail, you're out of luck. Apple isn't known for providing settings or options that only a small percentage of users will want, especially if it's a setting that might prove confusing in the future. 

Their UI designers likely weighed the number of users who don't want the button vs. the number of users who will be confused because their voicemail button is now missing and decided against the potential confusion. That certainly seems to be how they make most UI decisions.