This paper studies interval consensus for switched multiagent systems over directed networks, which consist of a continuous-time subsystem and a discrete-time subsystem regulated by a switching rule. Interval consensus refers to a state constrained consensus, where each agent is allowed to propose an acceptable interval to saturate their expressed states and the final consensus state lies in the nonempty intersection of all these intervals. We establish conditions guaranteeing interval consensus for switched multiagent system under arbitrary switching rules. Furthermore, we introduce the scaled interval consensus notion, which allows both the convergence of states to a pre-assigned proportion and the scaled consensus values lying in the desired range. Simulation results are provided to verify the effectiveness of the theoretical results.