This paper studies the distributed event-triggered model predictive control (DMPC) problem of coupled nonlinear systems with constraints. A novel event-triggered DMPC algorithm is proposed by designing a distributed event-triggering strategy and inventing a constraint that restricts the discrepancy between each subsystem's assumed and predicted states. With the designed triggering rule and constraint, the mutual disturbances caused by dynamical coupling are proved to be bounded, and the Zeno behavior is avoided. In addition, the suffcient conditions ensuring algorithm feasibility and closed-loop stability are provided. Finally, simulation studies are conducted to verify the effectiveness of the theoretical results.