The 19-year-old leaves Turf Moor with a solitary senior appearance to his name, featuring as a late substitute during the 2-1 npower Championship win at Doncaster last April.
McCarten played 16 times for Blue Square Bet Premier outfit Hyde FC this season, including five starts, scoring once.
A brief statement released by the Clarets read: "The club would like to thank Shay for his efforts and wish him well in his future career."
Manager Sean Dyche is ready to scour the transfer market to enhance his youthful squad despite a limited budget this summer, with local media reports suggesting Whitby Town goalkeeper Nick Liversedge could be on his way to Turf Moor following a successful trial appearance in last week's behind-closed-doors development squad friendly with Sunderland.
"I think it's going to be part of the current situation ongoing," he told the Lancashire Telegraph. "We have to look at, not really hidden gems, but any quality player we can find," s
"There's our home talent, of course, but that needs time to develop. The art of developing and coaching is very difficult to do overnight.
"It's part of the world that I'm used to before I got here, and I know it's part of the world here because of the resource base. But that doesn't stop you from being competitive."