The precise control of edge geometry and crystal shape of monolayer MoS2 is particular of importance for their applications in nanoelectronics and photo-electro catalysts. Here we reveal a crucial role of chemical potential in the determination of equilibrium shape (ES) and edge structure of monolayer MoS2 by using density-functional theory calculations. Applying Wulff construction rule, our results demonstrate the shape evolution of monolayer MoS2 flake from the dodecagonal shape, then to the hexagonal shape, to the triangular shape with the variation of chemical potential from the Mo-rich to the S-rich condition, and the edge structure of ES changes correspondingly from mixed zigzag/armchair edges to pure zigzag edges. This finding can be applied to explain extensive experimental observations about the morphology of MoS2 domains. Meanwhile, the edge magnetism and electronic structures of monolayer MoS2 domains are found to be dependent on their edge structure, which provides specific guidance for the magnetic modulation of monolayer MoS2 and designing more effective MoS2-based catalysts.