When the servers are shut down at the end of August, users will no longer be able to authorise new devices.
Microsoft began phasing out MSN Music in favour of the Zune Marketplace shortly after the company launched its portable media player in 2006.
The company revealed last week that it would take the authentication servers offline, citing the logistical headaches required to keep the servers up to date.
Users will be able to save their songs by burning them to an audio CD and then importing the songs as MP3s on the new player.
However, the EFF claims that, by shutting down the servers, Microsoft is betraying users who agreed to purchase the DRM-equipped songs.
In an open letter to Microsoft chief executive Steve Ballmer, EFF executive director Shari Steele described Microsoft's handling of the issue as "woefully inadequate ".
"Microsoft is asking its customers to invest more time, labour and money in order to continue to enjoy the music for which they have already paid," wrote Steele.
"What is worse, this suggestion could put customers at legal risk as they may not have documentation of purchase."
Steele has asked Microsoft to make a public apology, and recommended that the company either refund or replace the purchased songs with DRM-free tracks and work to remove DRM controls from the Zune store.
He warned Ballmer that Microsoft could lose the trust of its current crop of music customers if it fails to resolve the issue.
"While this announcement has directly affected MSN Music customers, users of other Microsoft products (particularly current and prospective Zune customers) are deeply concerned as well," wrote Steele.
"Your customers are forced to ask, if Microsoft treats its MSN Music customers so shabbily, whether there is any reason to suppose that it will treat other customers any better."
A spokesperson for Microsoft declined to comment or verify that the company had seen the letter.