This article devotes a practical finite‐time sampled‐data output consensus investigation for a class of nonlinear multiagent systems with unavailable velocities and undirected topology via output feedback. Noticing that the focused multiagent system features nonlinearities with non‐Lipschitz restriction, and the outputs of the agents are detectable only at the sampling instants, a reduced‐order observer with the sampled output measurement is established for each follower to evaluate the unavailable velocity, and the distributed finite‐time sampled‐data consensus protocols, which are constructed by the established reduced‐order observer as well as the sampled output measurement of the agents, are developed by combining the techniques of adding a power integral and backstepping. By selecting a suitable Lyapunov function candidate, we can verify that the developed sampled‐data consensus protocols which work under the allowable sampling period and the appropriate design parameters can solve the considered practical finite‐time output consensus problem. Finally, two simulation examples, include a numerical and an engineering simulations, are provided to reveal the effectiveness and availability of the proposed consensus scheme.