The 56-year-old author, who emigrated to Germany from then-communist Romania in 1987, made her debut in 1982 with a collection of short stories titled "Niederungen," or "Lowlands" in English, which was promptly censored by her government.
In 1984 an uncensored version was smuggled to Germany where it was published and her work depicting life in a small, German-speaking village in Romania was devoured by readers there. That work was followed by "Oppressive Tango" in Romania.
"The Romanian national press was very critical of these works while, outside of Romania, the German press received them very positively," the Academy said. "Because Mueller had publicly criticized the dictatorship in Romania, she was prohibited from publishing in her own country."
In 1987 she emigrated to Germany with her husband two years before dictator Nicolae Ceausescu was toppled from power amid the widening communist collapse across eastern Europe.
Mueller's parents were members of the German-speaking minority in Romania and father served in the Waffen SS during World War II.
After the war ended, many German Romanians were deported to the Soviet Union in 1945, including her mother, who spent five years in a work camp in what is now Ukraine.
Most of her works in German, but some works have been translated into English, French and Spanish, including "The Passport," ''The Land of Green Plums," ''Traveling on One Leg" and "The Appointment."
Mueller is the 12th woman to win the Nobel Prize in literature. Recent female winners include Austria's Elfriede Jelinek in 2004 and British writer Doris Lessing in 2007.
The prize includes a 10 million kronor ($1.4 million) prize and will be handed out Dec. 10 in the Swedish capital.