First install dconf-tools, if not :
sudo apt-get install dconf-tools
Second run dconf-editor :
dconf-editor
Browse to desktop.unity.panel to find the field : systray-whitelist and add gmusicbrowser to the list.
Before field contains, for instance :
['JavaEmbeddedFrame', 'Wine', 'scp-dbus-service', 'Update-notifier', 'clementine']
After field contains :
['JavaEmbeddedFrame', 'Wine', 'scp-dbus-service', 'Update-notifier', 'clementine','gmusicbrowser']
Suggestion for Quentin : Make gmusicbrowser modify this field during installation