In a takedown notice posted on RnBXclusive.com, SOCA claimed that the "majority of music files" that were available on the UK music exchange website "were stolen from the artists".
The message also warned anyone who has used the service to download music that they could face up to 10 years in prison and an unlimited fine under UK law.
It added: "SOCA has the capability to monitor and investigate you, and can inform your internet service provider of these infringements.
"You may be liable for prosecution and the fact that you have received this message does not preclude you from prosecution.
"As a result of illegal downloads young, emerging artists may have had their careers damaged. If you have illegally downloaded music you will have damaged the future of the music industry."
Police told the BBC that a man has been arrested on suspicion of fraud related to RnBXclusive.com, and bailed pending further inquiries.
In a statement, the agency said that activity connected to RnBXclusive.com can be attributed to the loss of around £15m a year in revenue to the music industry.
"SOCA targets organised criminal enterprises profiting from the exploitation of the UK public and legitimate businesses," said SOCA.
"Much of the music offered for download by the RnBXclusive.com website was illegally obtained from artists, leading the industry to attribute losses of approximately £15m per year to the site's activity."
SOCA said that the action was part of a wider push to combat illegal uploading of copyrighted material online.
RnBXclusive.com also operates Facebook and Twitter pages that are still available, although any links posted to its site just direct the user to the SOCA holding page.
Users have reacted with anger to the closure, including one writing "Screw SOCA!" on the RnBXclusive.com Facebook page. However, another added: "Am I the only one scared of this 10 year jail and fine?"
Legal journalist David Allan Green, known for the @jackofkent Twitter feed, questioned the legality of SOCA's move against RnBXclusive.com.
He tweeted: "Have pointed out to SOCA that third sentence of http://rnbxclusive.com (possibly nsfw) may be a contempt of court given second sentence...."
Another user explained: "The SOCA statement seems likely false since publishers/labels own most music, not the artists. Can only steal from the owner."
The shutdown comes as authorities worldwide launch a crackdown against online piracy, including the high-profile closure of the Megaupload website last month by US authorities, and the arrest of its founders, including Kim Dotcom.
> Kim Dotcom's home seized by police