N-enriched biochar can increase the accumulation of carbon (C), nitrogen (N), phosphorus (P), and biomass in rice plants. On the other hand, the biomass and C, N, and P contents of plant organs are important indicators to reflect plant C, N, and P storages. We established control, 4 t ha−1, and 8 t ha−1 N-enriched biochar treatment plots in a subtropical paddy field in China to investigate the effect of these treatments on C, N, and P storages, ecological stoichiometry in various rice plant organs, and their relationships with edaphic factors. The application of N-enriched biochar increased the biomass and storages of C, N, and P in rice roots, stems, leaves, and grains, mainly at 4 t ha−1. The application of N-enriched biochar decreased the C/N and C/P ratios of rice organs, but increased their N/P ratio. Changes in C/N were mainly due to the changes in storage, while N/P was positively correlated with N storage of stems, leaves, and grains and negatively correlated with P storage in roots. Pearson’s correlation analysis revealed that pH was negatively correlated, and soil N content was positively correlated with P storage in various organs of rice. In addition, soil P content and chlorophyll were positively correlated with N storage. In conclusion, we found that the application of N-enriched biochar improved plant N and P storage and stoichiometrical relations among rice organs.