In this paper, a nonlinear motorcycle model is considered in order to estimate both the lean and steering dynamics. The model is transformed into a Takagi-Sugeno (T-S) form using the well-known sector nonlinearity approach. The first contribution of this work is the exactness of the obtained T-S model compared to the considered nonlinear model, where the weighting functions of the T-S model depend on unmeasured state variables. A novel approach to construct a nonlinear unknown input fast observer is proposed. The objective is the simultaneous reconstruction of the state variables and the rider's torque. The observer's convergence is studied using Lyapunov theory guaranteeing boundedness of the state and unknown input estimation errors which is expressed by the Input to State Practical Stability (ISpS). Stability conditions are then expressed in terms of Linear Matrix Inequalities (LMI). Finally, simulation results are provided to confirm the suitability of the proposed nonlinear observer.