I believe this sensitive subject has come up before. Try looking through this thread which had a number of contributors for and against.
As I understand it, suicide is abhorrently wrong because of the worth of the human self and the *unseen* consequences of such an act. Murder is another form of extinguishing human life before its time, with equally massive consequences and we know from verse 5:5 *why* it is punished so severely under Divine law.
Some have pointed out that suicide in of itself is not addressed directly in the Quran. This may be the case, but even the word 'rape' is not mentioned directly in the Quran and yet we know the Quranic position on the mere *harassment* of women . Similarly I would say suicide and murder belong in the same boat.
That all said, just as there are shades of murder (e.g. manslaughter) there may be shades of suicide, e.g. accidental overdose, mental illness which of course would be judged on a case by case basis. In the Quran, the punishment for murder varies according to the shade (4:92). Interestingly, the Quran reminds us in the same verse that it should be impossible for a momin to kill another. Similar would be true of the impossibility of a momin committing suicide - but since in this case, the individual of the crime no longer remains on earth to face the consequences, his/her case must necessarily be decided by Allah.
See also my previous post on this subject: