Extension:PrivateDomains

The PrivateDomains extension restricts wiki editing to users with a certain e-mail address. It adds a new special page, Special:PrivateDomains, to allow changing the name of the organization and to add "trusted" e-mail addresses. Bureaucrats and staff members can access this special page.

If a non-privileged user (someone who does not have the organization's email address) tries to edit, s/he sees a warning box about the fact that s/he cannot change pages on the wiki. Be aware that the user can't view page sources either (IIRC).