I just found a solution for this problem:
First you have to install Lutris. You can find the instructions on https://lutris.net/downloads/.
After you've installed Lutris, go to https://lutris.net/games/minecraft/. Scroll down and click the Install button next to the LINUX New launcher version.
Then just go through the setup process.
After that you should be able to find the game on your desktop/application menu. Open Minecraft and login.
When you start the game, you should be able to go online.
Hope this helps