If that person fails to comply, EMusic will ask Napster to block the individual from the network.
Be careful when you are using Napster - someone might be watching while you are listening.
The company says anyone who gets involved in such activities will be traced and warned to stop, or face being banned from Napster.
In taking this action, EMusic is joining a growing number of organisations trying to impose constraints on the controversial pop-swapping system.
Large catalogue
Digital music website EMusic is one of many trying to make a living by selling digital downloads of pop music.
Visitors to its website can either pay a monthly subscription and download all the music they want, or pay by the album or single.
So far the site has amassed a catalogue of 140,000 songs by artists such as Elvis Costello, Phish and They Might Be Giants.
Now, in a bid to stop the pirating of tracks from its catalogue, EMusic has developed a system that can spot which of the millions of files available on Napster originated at the EMusic site.
Tracking watermarks
When it finds pirated files, EMusic plans to send an instant message to the person who put the track up for sharing, giving them 24 hours to remove it.
If that person fails to comply, EMusic will ask Napster to block the individual from the network.
In the past, Napster has said it would be happy to block people who were violating copyright laws.
EMusic is now seeding its songs with watermarks that make them easy to track on Napster.
"We're not interested in going after someone who makes a copy of a song for a friend," said Gene Hoffman, chief executive of EMusic. But if you make that song available via Napster, that is a violation of copyright law and that's what we're trying to stop."
Complex problem
The watermarking system will only be used to track the digital downloads available via EMusic.
The system will do nothing to protect the same tracks if they are copied from a CD someone bought in a store and then put on to Napster.
Napster is only part of the problem for digital music sites such as EMusic.
There are thousands of other places on the internet that MP3 files are being stored and traded. EMusic has no plans to go after those.
EMusic is only one of a growing group of people and organisations that is trying to make Napster less attractive to use.
Barking dogs
Journalist Michael Robinson, who is also lead singer of the rock band The Tabloids, has started a campaign called Stop Napster, which aims to seed the pop-swapping system with mislabelled or useless tracks.
Supporters of the Stop Napster campaign have been placing tracks on Napster that look like they are recordings of legitimate artists. They are actually a four-minute recording of dogs barking or contain anti-piracy messages read by Charlton Heston.
In a similar vein, the Cuckoo's Egg project is also trying to sow distrust among Napster users by lodging mislabelled tracks.
Instead of dogs barking, downloaders may hear 30 seconds of the music they were expecting. But after that, they get nothing but the sounds of a cuckoo clock, or a series of random uncopyrighted sounds.
Jon and Michael Fix, who started the Cuckoo's Egg project, said they were not trying to shut down Napster but just wanted to "promote debate regarding online file trading and artists' rights in the digital age".