This article investigates observer‐based consensus issues for a class of Lipschitz nonlinear multi‐agent systems (MASs) with unknown input. To address the challenges because of the unmeasurable states and the unknown input of each agent system, an interval observer is utilized to design an unknown input observer (UIO). The UIO possesses the capability of generating asymptotically the estimations of both the system states and unknown input simultaneously. Subsequently, a distributed control protocol scheme is put forwarded. The distributed controller for each agent is designed by using the state estimation and the unknown input reconstruction (UIR). The unknown input is compensated thanks for the introduction of the UIR into the controller, and thus leads to a better control performance. Besides, the event‐triggered strategy is also considered such that agents communicate with each other discontinuously. In this way, an observer‐based event‐triggered distributed control protocol scheme is developed, and under the scheme, the asymptotic convergent MASs consensus is accomplished. Finally, the effectiveness of the proposed methods is verified by a simulation example.