The study reviewed here strongly suggests that regularly drinking even small amounts of alcohol increases the risk of many types of cancer -- including breast cancer -- in women.
Women who drink wine, beer, or liquor increase their chances of getting breast cancer by about 30%, according to a report in Cancer Epidemiology, Biomarkers and Prevention (Vol. 10, No. 12: 1281-1285). Marji McCullough, ScD, RD, nutritional epidemiologist at the American Cancer Society (ACS) said "They find that people who drink more have increased risk for breast cancer. Most studies have shown that alcohol has a stronger effect on post-menopausal breast cancer."
Other studies have shown that hormone-receptor-positive breast cancer is the type of breast cancer most affected by alcohol. Estrogen can cause hormone-receptor-positive breast cancer to grow and alcohol can increase the amount of estrogen in a woman’s body. This increase in estrogen may be part of the reason for the link between alcohol and breast cancer risk

Source: even a few drinks a day increases cancer risk in women.