This paper deals with the state estimation problem of a class of nonlinear time-varying systems with switched dynamics. Based on the concept of fixed-time stability, an observer is designed to reconstruct the continuous state of switched nonlinear time-varying systems with state jumps, satisfying the minimal dwell-time condition. Using the past input and output values of the studied system, some sufficient conditions are provided to estimate the state before the next switching. Some numerical results illustrate the effectiveness of the proposed scheme.