This article investigates the containment control for state-constrained multiagent systems. Existing results assume that the dynamic of the multiple leaders is known as prior knowledge. First, a distributed adaptive observer is used to estimate the leader's unknown parameters. The local reference signal and its high-order derivatives are generated by an $n$th-order filter, which will be employed in the backstepping design procedures. Second, a log-type nonlinear state-dependent barrier function is established to cope with the time-varying asymmetric full-state constraints. The constrained system is equivalently transformed into a nonconstrained one. Finally, a distributed adaptive fuzzy containment control scheme is developed for the nonconstrained system. Only one adaptive law is required in each distributed controller, and no feasibility conditions and partial-derivative terms are involved in the virtual and actual controllers. In addition, the time derivatives of the candidate Lyapunov functions are guaranteed to be negative semidefinite by introducing a series of reduced-order smooth functions. It is proved that the containment error converges to a user-predefined interval, and all the signals in the closed-loop system are bounded. The time-varying asymmetric full-state constraints imposed on the followers are not violated. Two illustrative examples demonstrate the effectiveness of the suggested approach.