Minecraft has sold nearly 4.5 million copies on Microsoft's Xbox Live Arcade platform.
Mojang's first and most famous game, created by studio founder Marcus 'Notch' Persson, was originally created for PC where it has sold over 8.2 million copies.
The console port of the game was made by Scottish developer 4J Studios.
Minecraft is the third most played game on Xbox Live, beaten only by Call of Duty: Black Ops 2 and Halo 4.
According to figures provided to Gamasutra, the Xbox version has sold between 40-60,000 copies a week during the November period.