The portable version of Minecraft can be purchased for $7 (£4.30) from Amazon's AppStore and is compatible with the firm's Kindle Fire tablet.
The recently announced 7-inch Kindle Fire HD and upgraded Kindle Fire will release in the UK on October 25.
Both models can be pre-ordered from Amazon, costing £159 and £129 respectively.
Minecraft Pocket Edition, meanwhile, is also available for iOS and Android devices through the App Store and Google Play.
Minecraft debuted on PC in November last year following an extended beta period. An Xbox 360 port was released earlier this month, selling 1 million copies in just five days.
Mojang was forced to hand out refunds to customers with standard definition television sets who purchased the Xbox 360 edition as it was not clearly indicated that multiplayer mode is incompatible with the technology.
Minecraft: Xbox 360 Edition holds the record for most first-day sales on Xbox Live Arcade.
> Read Digital Spy's review of 'Minecraft: Xbox 360 Edition'
Watch a trailer for Minecraft: Xbox 360 Edition below: