(1) Background: Individuals with BRCA1/2 gene mutations are at increased risk of breast and ovarian cancer. The prevalence of BRCA1/2 mutations varies by race and ethnicity, and the prevalence and the risks associated with most BRCA1/2 mutations has not been unknown in the Vietnamese population. We herein screen the entire BRCA1 and BRCA2 genes for breast and ovarian cancer patients with a family history of breast cancer and ovarian cancer, thereby, suggesting a risk score associated with carrier status and history for aiding personalized treatment; (2) Methods: Between December 2017 and December 2019, Vietnamese patients who had a pathological diagnosis of breast and epithelial ovarian cancer were followed up, prospectively, after treatment from two large institutions in Vietnam. Blood samples from 33 Vietnamese patients with hereditary breast and ovarian cancers (HBOC) syndrome were collected and analyzed using Next Generation Sequencing; (3) Results: Eleven types of mutations in both BRCA1 (in nine patients) and BRCA2 (in three patients) were detected, two of which (BRCA1:p.Tyr1666Ter and BRCA2:p.Ser1341Ter) have not been previously documented in the literature. Seven out of 19 patient’s relatives had BRCA1/2 gene mutations. All selected patients were counselled about the likelihood of cancer rising and prophylactic screening and procedures. The study established a risk score associated with the cohorts based on carrier status and family history; (4) Conclusions: Our findings suggested the implications for the planning of a screening programme for BRCA1 and BRCA2 genes testing in breast and ovarian cancer patients and genetic screening in their relatives. BRCA1/2 mutation carriers without cancer should have early and regular cancer screening, and prophylactic measures. This study could be beneficial for a diverse group in a large population-specific cohort, related to HBOC Syndrome.