The invention of the maser stimulated revolutionary technologies such as lasers and atomic clocks. Yet, realizations of masers are still limited; in particular, the physics of masers remains unexplored in periodically driven (Floquet) systems, which are generally defined by time-periodic Hamiltonians and enable observation of many exotic phenomena such as time crystals. Here, we investigate the Floquet system of periodically driven 129Xe gas under damping feedback and unexpectedly observe a multimode maser that oscillates at frequencies of transitions between Floquet states. Our findings extend maser techniques to Floquet systems and open avenues to probe Floquet phenomena unaffected by decoherence, enabling a previously unexplored class of maser sensors. As a first application, our maser offers the capability of measuring low-frequency (1 to 100 mHz) magnetic fields with subpicotesla-level sensitivity, which is substantially better than state-of-the-art magnetometers and can be applied to, for example, ultralight dark matter searches.