The women from the site of the worst massacre during Yugoslavia's bloody collapse, accused Handke of being a Serb apologist during the 1990s wars.
The Swedish Academy's pick last month triggered outrage in the Balkans and beyond because of Handke's admiration for late Serbian strongman Slobodan Milosevic.
In the 1990s, the Austrian writer emerged as a vocal defender of Serbs as Yugoslavia broke apart.
On Tuesday several dozen women gathered in protest outside Stockholm's embassy in Sarajevo, where Sweden's Crown Princess Victoria and her husband Prince Daniel are currently paying a visit.
The women plan to protest weekly until the Nobel ceremony on December 10th when Handke, 76, will receive his prize.
Some women held up photos of the writer from a personal visit he made to Srebrenica, the hamlet where some 8,000 Bosnian Muslim men and boys were slaughtered by Bosnian Serb forces in July 1995.
The novellist is seen standing in front of a sign at the entrance to the town, less htan a year after the killings, according to the women.
The group also gave the Swedish ambassador a letter for the king and queen, asking them to “prevent the shame, not only of the Swedish people”, but also “shame of civilization”.
“We do not agree with awarding of the prize to someone who supported crimes and genocide,” Munira Subasic, president of the association of mothers of victims from Srebrenica, told reporters.
“The Nobel Prize for Handke is a vote in support of our humiliation” by genocide deniers, the letter said.
In 1997 Handke was accused of minimizing Serb war crimes in his book A Journey to the Rivers: Justice for Serbia.
He also drew criticism for speaking at the 2006 funeral of Milosevic who died awaiting trial for genocide, war crimes and crimes against humanity.