This study explores the design of an unknown input observer for discrete-time nonlinear Markov jump systems based on Lyapunov theory and Takagi-Sugeno fuzzy models. Firstly, the nonlinear system is transformed into a linear system using linear system theory and the Takagi-Sugeno fuzzy model is applied to solve the nonlinear problem. Then, under the conditions where unknown inputs exist in the state equations of the nonlinear Markov jump system, an unknown input observer is proposed so that the error system for state estimation has no relation to the unknown inputs. The feasibility conditions of the unknown input observer steady-state estimation error system are derived to ensure that the estimation error can approach zero. Additionally, linear matrix inequalities are used to address the feasibility problem of unknown parameters. The introduction of relaxation matrices reduces the conservativeness of the conditions. Finally, the proposed unknown input observer is validated using the vehicle lateral dynamics system. The results indicate that the unknown input observer can accurately track the actual state of the system, and the corresponding estimation errors converge to zero.