Minecraft - a construction game in which players can build nearly anything imaginable, block by block, in a digital, Lego-like world - has spread like wildfire since its full release by developer Mojang in 2011.
Minecraft is the top paid-for app both on Apple Inc's  iOS and Google Inc's Android systems and helped Mojang, which employs just 40 people, bring in 2.05 billion crowns ($287 million) in revenue in 2013, giving it an 896 million crown ($126 million) operating profit for the year.
Director of website Gamesbrief Nicholas Lovell described Minecraft as a hugely successful product which has "captured the imagination of pretty much everybody under the age of 15", saying the game could help Microsoft broaden its appeal.
While the Mojang team will join Microsoft studios behind global franchises such as "Halo" and "Fable", its three co-founders, who have been chased by the likes of Napster co-founder and early Facebook Inc investor Sean Parker, will be leaving to start new projects.
As if to erase any doubts about the importance of gaming, Microsoft CEO Satya Nadella said it was a "top activity" spanning devices from PCs and consoles to tablets and mobiles,  with billions of hours devoted to it each year.
"Minecraft is more than a great game franchise - it is an open world platform, driven by a vibrant community we care deeply about, and rich with new opportunities for that community and for Microsoft," Nadella said on Monday.
Microsoft has spent lavishly in the Nordic region in recent years, buying the handset business of Nokia for $7.2 billion in a deal which closed this year. In 2011, it spent $8.5 billion on Skype, which has its roots in Scandinavia and the Baltics.
Some analysts were positive about the acquisition.
"The news robustly dismisses the idea that games are no longer at the core of Microsoft's strategic direction and also underlines the growing importance of independent titles alongside big-budget games," Piers Harding-Rolls, head of games at IHS Technology, wrote in a note.
FBR Capital Markets said the deal gave Nadella "the right product at the right time," as Microsoft invests in its Xbox strategy and moves into the intensely competitive mobile phone sector with Nokia under its hood.
Just five years old, Mojang was co-founded by Markus Persson, who developed the hit Minecraft game after previously working at Sweden's King Digital Entertainment Plc, maker of the Candy Crush Saga game.