Rice (Oryza sativa L.) is a globally important cereal crop. Sodium (Na+) and potassium (K+) are the major monovalent ions which affect rice growth, and exploring their uptake mechanisms will be useful for understanding rice biology. Since the balance of Na+ and K+ plays a significant role in adaptation of rice to salinity, that biology might inform the search for tolerance. In this study, the Na+ and K+ concentration and Na+/K+ ratio in grains and shoots were analyzed in the Bengal and Assam Aus Panel grown in field conditions under continuously flooded (CF) and alternate wetting and drying (AWD) irrigation. Overall, AWD irrigation significantly reduced the Na+ concentration and increased the K+ concentration in shoots and grains compared to the plants grown under CF. Genome-wide association mapping was conducted on Na+, K+ concentration and Na+/K+ ratio with 2 million SNPs using an efficient mixed model. Only QTLs which contained more than two significant SNPs (p < 0.0001) and where at least one of these significant SNPs passed a 10% false discovery rate were reported. A total of 106 QTLs were identified as being associated with Na+ concentration and Na+/K+ ratio across all traits and field conditions, with 48 QTLs found in multiple traits and/or water conditions. Four notable QTLs (one each on chromosomes 1 and 11, two on chromosome 2) and the haplotype variants of four candidate genes (OsHKT1;5, OsNHX2, LOC_Os02g32490 and OsFAD2_1) are discussed. The QTLs/candidate genes identified here could be useful for breeding rice that accumulates lower concentrations of sodium.