Now with Gnome in Ubuntu 18.04 how to Integrate wine systray with real one
You can use the Tray Icons extension by zhangkaizhao.
TopIcons, which sjuk's earlier answer recommends, doesn't work anymore.
Tray Icons is based on an older extension, TopIcons Plus, which is similar to TopIcons. As the Tray Icons README says:
Tray Icons
Simple version of TopIcons Plus.
Base on TopIcons Plus v22 from GNOME Shell Extensions.
Keep it as simple as possible.