Grbavica is Zbanic's first feature length film
Grbavica, by director Jasmila Zbanic, looks at the aftermath of the mass rape of women during the siege of Sarajevo in the Bosnian war.
British directors Michael Winterbottom and Mat Whitecross were awarded the Silver Bear for best director, for their film, Road to Guantanamo.
It tells the true story of three British Muslims caught in Afghanistan and who end up at Guantanamo Bay.
This year's festival appears to have an overtly political theme.
"War in Bosnia was over some 13 years ago and yet war criminals Radovan Karadzic and Ratko Mladic (former Bosnian Serb leader and army commander) still live in Europe freely," Ms Zbanic said.
"They've not been captured for organising the rape of 20,000 women in Bosnia. This is Europe and no one is interested in capturing them," she added.
Michael Winterbottom dedicated his award to the three men which inspired his film.
The head of the jury, British actress Charlotte Rampling, said this year's films "reflected the mood of the world today".
Two films won the Silver Bear: Offside, by the Iranian director Jafar Panahi, a drama about a girl who has to disguise herself as a boy to watch a football match, and Danish-Swedish film A Soap about a woman's relationship with a transsexual.Silver Bear awards for best actors went to two Germans - Moritz Bleibtreu for his role in the film Elementary Particles, and Sandra Hueller for her part in Requiem.