Sony said Wednesday it would permanently block PlayStation 3 owners from the PlayStation Network if they are using jailbroken consoles.

Access to what Sony describes as a “world of entertainment” will be “terminated permanently,” the Japanese entertainment concern announced.

“To avoid this, consumers must immediately cease use and remove all circumvention devices and delete all unauthorized or pirated software from their PlayStation 3 systems,” Jeff Rubenstein, the company’s social-media manager, said in a blog post.

Sony did not return a message seeking comment about details on how it would...