The low-budget production, a harrowing film about illegal abortion in communist-era Romania, had already taken the top award earlier this year at the Cannes Film Festival.
"I'm very honored by the award," said Mungiu, who also took the best director award for the film.
Among the other 17 awards given, German director Fatih Akin's "The Edge of Heaven" won best screenplay. Akin wrote and directed the film, a German-Turkish cross-cultural tale of loss, mourning and forgiveness, and a follow up to his critically acclaimed "Head On," which won the Berlin festival's top prize in 2004.
The film was a big favorite at Cannes, and took the prize for the best screenplay there as well.
Helen Mirren won best actress for her portrayal of Queen Elizabeth II in "The Queen" - for which she had already won an Oscar - while Sasson Gabai won best actor for his work in "The Band's Visit."
French filmmaker Jean-Luc Godard was honored by the European Film Academy with a lifetime achievement award.