Microgrids can effectively integrate renewable energy sources (RESs) and provide power for local customers. However, uncertainties of RESs and loads pose challenges to microgrid operation. The traditional point optimization method is unrealistic, and the widely used stochastic optimization (SO) method is time-consuming. Besides, battery energy storage systems (BESSs) are critical dispatchable devices to alleviate adverse effects of uncertainty, so an accurate nonlinear degradation cost model of BESSs should also be proposed. To handle such problems, the paper proposes an affine–arithmetic (AA)-based microgrid interval optimization (IO) method considering uncertainty and BESS degradation. First, the AA theory is introduced to model the RES and load variation ranges as intervals and calculate the interval uncertainty. Then, a nonlinear BESS degradation cost model is proposed, which can assess battery degradation costs considering different charging and discharging behaviors. The nondominated sorting genetic algorithm-II (NSGA-II) is employed to solve the proposed microgrid IO framework. For validation, the proposed IO method was compared with the point optimization method and SO method under various uncertainty realizations in a modified IEEE 33 bus system. The simulation results indicated the effectiveness of the proposed IO method in terms of an equilibrium between the simulation time and optimization performance.