In answering this, first we'll need to define "member directory". We think of this as a front-end system on your site which allows members to see information about other members. 

In the above context, MemberMouse does not include member directory features. 

However, MemberMouse creates a WordPress user for every member, and this is what third-party directory plugins typically utilize. One of our Implementation Partners, MemberDev, offers fully integrated member directory functionality as part of their MemberMouse Done for You offering.

There is also a plugin called Dynamic User Directory which could fulfill this need.

Note that MemberMouse data is stored in custom tables, and not very much data is natively available in the User Directory. In the case of this plugin, here are the fields from MemberMouse that it can natively display:

We can facilitate the process of custom work by providing information to the developer on how MemberMouse structures the member information it stores.