The award was announced at the end of the GameCity festival in Nottingham, and chosen by a panel that included UK figures from film, TV and politics.
Other games in the running included Portal 2. "It's a great honour to be compared to those games," said game developer Markus Persson to the BBC. Persson runs Sweden's Mojang company, which publishes Minecraft.
Despite officially being in the test, or 'beta' stage, Minecraft has sold four million copies around the world. In the block-based game players have to construct tools and a home from basic materials, and survive the monsters that come out at night.
One of the judges, Ed Hall, told the BBC that Minecraft "just wasn't like anything else... it felt like it had an expanding life of its own. It had an organic nature... It's simplistic and addictive, and there's an element of beauty in what you are doing."
The only reservation was felt by jury member Nitin Sawhney, a famed composer of electronic music, who thought that the game's soundtrack left something to be desired, reports BBC news.