This is an extension that adds a button to gnome panel which when clicked launches Firefox Profile Manager.
‘firefox -no-remote -profilemanager’ is the command that is actually executed.

[Note: This extension isn't maintained any more.]

Installation Instructions:

Download:
cd ~/.local/share/gnome-shell/extensions
git clone https://github.com/xtranophilist/gnome-shell-extension-firefox-profiles.git
mv gnome-shell-extension-firefox-profiles/ firefox-profiles@xtranophilist

Restart Gnome:
Alt+F2 to open run command prompt
Enter r

Enable ‘Firefox Profiles Chooser Extension’ from Extensions from gnome-tweak-tool

The extension is available as github repo.