According to a recent study published in the journal Cancer, Epidemiology, Biomarkers & Prevention, regular use of aspirin or other pain relievers in postmenopausal women leads to lower estrogen levels, which could contribute to a reduced risk of breast and ovarian cancer.
The researchers from Harvard University studied the link between aspirin and other NSAID medications and concentrations of estrogen in 740 postmenopausal women.
Average estrogen levels were more than 10% lower among women who regularly took aspirin and NSAIDs.
Levels in those who regularly took aspirin, NSAIDs and the painkiller acetaminophen were 15.2% lower than the participants who did not regularly take the drugs, the researchers said in a statement, adding that a trial is needed to determine if aspirin and other pain relievers could prevent certain cancers in women.

Yes, aspirin has proved to reduce risk of Ovarian Cancer. But, if womens include healthy diets in their life style, risk for Ovarian Cancer can be reduced even more. Include vegetables like kale, broccoli, cauliflower, red meat, processed meat, and cured meat in everyday life, it will definitely help.
http://www.justcancer.org/ovarian-cancer-diagnosis.html