Telltale Games and Mojang have joined forces and announced Minecraft: Story Mode - A Telltale Games Series. It's a standalone experience in typical Telltale Games fashion, but it will be very "minecrafty" nonetheless.
"We're not intending on creating an "official" story for Steve, or explaining the world of Minecraft in detail. It will be a cool game."
Minecraft: Story Mode - A Telltale Games Series will launch in 2015 on a multitude of platforms (and yes, that includes PlayStation consoles).