My friend used a mobile app where he could log in and chat in the server. The app allows him to send emoji characters, but when I receive them in my Minecraft (the game) client, an empty message appears after his username in chat, like sending a whitespace-character in some chat programms.

I guess either the server or the client should check whether or not the character is render-able with the current font. If it is not; don't display it (and maybe let his client know his message was invalid as well?)

(edit) I guess it's this app he used:
http://www.minecraftforum.net/forums/mapping-and-modding/minecraft-tools/1264022-android-minecraft-chat-app

(new issue because a mod closed it without testing)
How to reproduce without third party software:

1. Copy an emoji character to your clipboard. (optional)
2. Paste it in chat (you won't see it) or otherwise input an emoji character.
3. Hit Enter
4. You now have an invisible message in chat.