The National Academy of Recordings Arts and Sciences (NARAS) says the service enabled users to trade copyrighted music files from the awards show.
Within hours of the awards being handed out, music files of performances from the show, including Sir Elton John's controversial duet with Eminem, could be downloaded via Napster.
Michael Greene, president and chief executive of NARAS, said the suit filed in a San Francisco federal court sought monetary damages for millions of dollars lost because of online trading activity via Napster.
'Re-evaluating'
"The day following the Grammy Awards we were in the recording studio remixing all of this stuff with the intention of putting it out [as a recording], only to find that all of the audio was already up on Napster, and there had been millions of downloads," Mr Greene said.
The duet pairing veteran Sir Elton John with Eminem might never now be commercially released, he added.
"We are re-evaluating in light of Napster giving it away to hundreds of thousands of people," Greene said.
Grammy Award show performances ranging from Madonna's Music to U2's Beautiful Day were available through the service within hours of the show's broadcast on 21 February.
Block
Napster is a software program that allows registered users to source computer music files from the hard drives of potentially millions of other users.
While no music files are downloaded from Napster itself, the program acts as a form of search engine for the files.
The song swapping service was ordered by a US federal judges this week to block copyrighted music from its site.
The judge gave Napster 72 hours to block the songs and the service has agreed to comply with the order.