Called Minecraft: Story Mode, it will be an episodic game set in the familiar Minecraft world but will introduce some new characters into the setting.
The game is being made by Telltale Games which has produced several other episodic titles.
The first episode is due to be released in 2015 on consoles, PCs, Macs and Android devices.
So far, little information about what it will be like have been released. Mojang has produced a short browser-based game called Info Quest II to explain what it might be like.
In a blogpost, Mojang said the game would be developed with the help of the Minecraft community.
It sought to reassure players that Story Mode would not be like the violent and bloody games Telltale has produced before now. Recent Telltale games include The Wolf Among Us, Tales from the Borderlands and titles based on Game of Thrones and zombie thriller The Walking Dead.
"Telltale's game will feel similar in tone to Minecraft itself," said Mojang, "though it's a totally original take inspired by our game."
The news about Story Mode comes soon after Mojang released a finished version of its Scrolls card-based magic battling game.