If the company, broadband service provider ePhone, fails to comply with the order from the Solna District Court to hand over information about the users connected to certain IP-addresses, it will face 750,000 kronor ($95,000) in fines.
The court found that there is probable cause to believe that ePhone users were violating copyrights and that the company should pay the publishers' court costs of 75,000 kronor.
When the new Swedish law came into force on April 1st, five publishers of audio books were the first copyright holders to file a case under the new measure.
The publishers, which include 15 authors who suspected their work has been spread illegally over the internet, demanded to know who owned a server suspected of containing some 2,000 audio book titles.
But ePhone refused to reveal who was using the IP-address in question, pointing out that a password was required in order to gain access to the works stored on the computer
As a result, the company argued, the sound files weren't publicly accessible and thus the matter wasn't a case of copyright infringement.
The publishers then sought a court order which would force ePhone to divulge information about the users tied to the IP-address.