Breast cancer (BC) is a multifactorial disease and the most common cancer in women worldwide. We describe a machine learning approach to identify a combination of interacting genetic variants (SNPs) and demographic risk factors for BC, especially factors related to both familial history (Group 1) and oestrogen metabolism (Group 2), for predicting BC risk. This approach identifies the best combinations of interacting genetic and demographic risk factors that yield the highest BC risk prediction accuracy. In tests on the Kuopio Breast Cancer Project (KBCP) dataset, our approach achieves a mean average precision (mAP) of 77.78 in predicting BC risk by using interacting genetic and Group 1 features, which is better than the mAPs of 74.19 and 73.65 achieved using only Group 1 features and interacting SNPs, respectively. Similarly, using interacting genetic and Group 2 features yields a mAP of 78.00, which outperforms the system based on only Group 2 features, which has a mAP of 72.57. Furthermore, the gene interaction maps built from genes associated with SNPs that interact with demographic risk factors indicate important BC-related biological entities, such as angiogenesis, apoptosis and oestrogen-related networks. The results also show that demographic risk factors are individually more important than genetic variants in predicting BC risk.