Board Thread:Support Requests - Community Management/@comment-15441538-20130823132530/@comment-1929113-20130824023450

Sophia McLaren-Cobb wrote: By default, the non-logged-in users' IP addresses are already hidden. Unless you have ShowAnonIP from Dev Wiki, then the IP addresses will not show. Like usual, have them make an account to permeanently hide their IP.

While you might not see them just by browsing Wiki Activity, the IP addresses still show by looking at the RecentChanges or by going to their contributions page.

It is not possible to completely hide anon user's IP addresses in MediaWiki.