The Red River Delta (RRD), including 11 provinces, is one of the four largest rice-growing areas in Vietnam. Tropical storms often occur and cause serious flooding from May to October annually in the RRD, which strongly affects the productivity of the summer–autumn rice, one of two main rice crops. Therefore, the rapid assessment of damaged rice area by flooding inundation is critical for farmers and the government. In this study, we proposed a methodology for quick estimation of rice areas damaged by flooding using Sentinel 1A (S1A) imagery. Firstly, the latest rice map was produced. Then, a Near Real-Time (NRT) flood map, which is estimated from S1A images at the closest time to a flooding event, was generated by excluding the yearly permanent map from the temporal water map. Our experiment was conducted for the assessment of damaged rice area by flooding from the tropical storm named Son-Tinh, which happened on 19–21 July 2018. A Support Vector Machine (SVM) classifier was applied on time-series of S1A VV with VH data (VVVH) to obtain a rice map for the winter-spring season of 2018 with 90.5% Overall Accuracy (OA) and 2.37% difference (12,544 ha) from the General Statistics Office (GSO) of Vietnam’s reports for the whole region. Then, the Otsu thresholding method was applied for permanent water surface extraction and NRT flood mapping. The estimated damaged area was compared to available provincial and communal statistics for validation and further analysis. Right after the Son-Tinh storm, the estimation of inundated rice was approximately 50% of the total rice area in the RRD (271,092 ha). As a result, rice damage level strongly corresponds to the inundation period. In addition, the rice-flooding frequency map over the RRD was estimated to show rice fields suffering a high risk of flooding during the rainy season in the RRD. Our experiment’s results highlight the potential of using Synthetic-Aperture Radar (SAR) imagery for fast monitoring and assessment of paddy rice areas affected by flooding at a large scale in the RRD region.