Extensions are not disabled in Private Browsing mode.

It seems my question was not clear. I don’t want to run a particular extension in normal mode (in normal mode that extension should be disabled) but while using private mode the extension should me enabled. Is it possible to do it in Firefox? I know its an odd request!

That is not possible. Extensions are either enabled or disabled.

You can consider to use two profiles and run a second profile in PB mode with the extensions that you want to use in PB mode.

See:

• https://developer.mozilla.org/Mozilla/Multiple_Firefox_Profiles

You can add -no-remote to the command line to open another Firefox instance with its own profile and run multiple Firefox instances simultaneously.

• http://kb.mozillazine.org/Opening_a_new_instance_of_Firefox_with_another_profile