This paper addresses the prescribed-time (PT) output-feedback control of uncertain nonlinear systems. Different from previous PT theorems tailored for full-state feedback frameworks, a novel PT Lyapnove stability theorem is proposed for output-feedback framework to handle the challenging redundant terms stemming from state observer and unknown nonlinearities. We then construct a PT state observer and integrate it with the backstepping control design. The resulting PT output-feedback control ensures that all system states and observer states converge to zero in the PT interval, irrespective of initial conditions or control parameters. Finally, two simulation results are given to illustrate the effectiveness of our theoretical finding.