This paper investigates the fixed-time output consensus problem for a class of second-order multi-agent systems with unknown nonlinearities under switching communication topologies, utilizing fixed-time quasi-passivity theory. First, the concept of fixed-time quasi-passivity for nonlinear systems is proposed. It is proven that the states of a fixed-time quasi-passive system are bounded and converge to a bounded set within a fixed time, thereby establishing a criterion for fixed-time quasi-passivity. Second, for the multi-agent system containing unknown nonlinear functions, fuzzy logic systems are employed to approximate the unknown nonlinearities, and a fuzzy adaptive fixed-time quasi-passivity controller is designed. This ensures that the multi-agent system achieves fixed-time quasi-passivity under switching topologies.The obtained fixed-time stability criterion is then used to prove the fixed-time output consensus of the multi-agent system. The controller design method effectively avoids the singularity issue inherent in traditional backstepping by incorporating a nonsingular function to design virtual controllers. Finally, simulation results are provided to validate the effectiveness of the proposed approach.