The GeoIP database is a binary file that you download from the MaxMind site, re-name, and then copy to the /misc directory of your Piwik installation. The code to use this binary file was adapted from the MaxMind API, and is built into Piwik.
Thus, your Piwik installation doesn’t actually need to connect directly to the MaxMind server. You might want to configure Piwik to not try to update its copy of the MaxMind database automatically. MaxMind releases monthly updates to the database in the first week of every month.
Here’s the download location:
Download the GeoLite City binary/GZIP file, unzip it, rename the result to GeoIPCity.dat, and then copy that re-named file to the server’s /misc directory in the Piwik install. Of course, you’ll need to activate the PHP method of Geolocation