A takedown notice warned visitors who have used the site to download music they could face up to 10 years imprisonment and an unlimited fine.
Soca said music posted on the site was "stolen from the artists" and may have "damaged careers".
A man has been arrested for fraud and bailed pending further enquiries, police told the BBC.
"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 added that the action was part of a wider operation combating illegal uploading of copyrighted material online, with several sites being targeted using "varied techniques".
Some industry observers believe the action is a fresh sign that British authorities are stepping up efforts to stamp out online piracy.
However, Loz Kaye, leader of the Pirate Party UK, said he disagreed with the nature of the closure.
"The explicit threat to visitors of the site and take down notice is alarming.
"The claim that the information gathered can be used to identify visitors and their location, followed by a statement that Soca has the capability to monitor, investigate and inform visitors internet service providers of apparent 'infringements', making visitors liable for prosecution seems extreme and unduly threatening.
http://www.bbc.co.uk/news/technology-17039722