This article investigates the finite-time containment control problem for fractional-order nonlinear multiagent systems (FOMASs) with event-triggered inputs. First, a new Lyapunov stability lemma is developed, which provides a basic approach for the completely unknown nonlinear fractional-order system to realize finite-time convergence. Considering the containment control for FOMASs, the restricted assumption that the derivatives of leaders’ trajectories are known to the followers is removed, and only the boundedness of derivatives is required in this article, whose upper bound need not be known. To reduce the burden of communication, an event-triggered condition consisting of the control input and a decreasing function related to the containment errors is devised, which can provide more design freedom to balance the system performance and communication resources. According to the proposed fractional-order finite-time convergence lemma, a distributed adaptive containment control scheme is developed, such that each follower can be steered to the convex hull spanned by the leaders in finite time. Simulation examples further demonstrate the effectiveness of our proposed method.