I discovered that mod_auth_mysql has been replaced with mod_auth_dbd on Centos 7 and Apache 2.4. The following is a quick reference to setting mod_auth_dbd up

<VirtualHost 10.10.10.10:80>
  # tell DBD you are using mysql
  DBDriver mysql
  # how to access the database that contains the usernames and passwords
  # host = server running the sql server. Can be ip address or FQDN
  # dbname  = name of the database that contains the table that has the users
  # user = username that has at least read access to the table that has the users
  # pass = password of the above user
  DBDParams "host=localhost dbname=WebUsers user=WebUserDBAdmin pass=L3tM30ut"
  # Minimum number of connections
  DBDMin 4
  # Maximum sustained number of connections
  DBDKeep 8
  #Set the hard maximum number of connections per process
  DBDMax 20
  # Set the time to keep idle connections alive when the number of connections specified in DBDKeep has been exceeded
  DBDExptime 300
  <Directory /opt/MyWebSite>
    #sql querry that will return the password for the selected user
    # passwords should be stored the database using the mysql "encrypt" function
    AuthDBDUserPWQuery "select user_passwd from users where user_name=%s"
    <RequireAll>
      AuthType Basic
      AuthName "My Web Site"
      Require valid-user
      AuthBasicProvider socache dbd
    </RequireAll>
  </Directory>
  (other parameters as needed)
</VirtualHost>

For more information, see https://httpd.apache.org/docs/2.4/de/mod/mod_dbd.htm and https://httpd.apache.org/docs/2.4/mod/mod_authn_dbd.html.