Reference: http://www.alfawzan.af.org.sa/node/14742
Question: What is the ruling about offering the [funeral] prayer for the one who has committed suicide?
Response: The [funeral] prayer is to be performed over him, since he is a Muslim. However, the people of virtue are not to [perform the funeral] prayer over him – as a mark of rejecting what he did, and deterring the likes of him. As for the rest of the Muslims, they are to perform the [funeral] prayer over him, and it is not permissible to leave him be without offering the [funeral] prayer because he is a Muslim – even if he committed a major sin, he is still a Muslim.