This study presents the results of an investigation into the magnetocaloric effect (MCE) in the Ni47Mn40Sn13 alloy under the influence of alternating magnetic fields. The study examines the dependence of the MCE on temperature (ranging from 80 to 350 K), magnetic field (up to 8 T), and frequency (1–20 Hz). The maximum values of the MCE observed near the phase transformation temperatures have different signs depending on the type of phase transition, with approximately equal values |ΔTad|≈3.2 K in a field of 8 T. The field dependence of the MCE in the vicinity of the magnetic phase transition is described by an expression of the form ΔTad ~ α⋅Tn, where n = 1 at T < TC, n = 2 at T > TC, and n = 2/3 at T = TC, which is consistent with theoretical predictions. The study also finds that the field dependences of the MCE in the region of the martensitic phase transition show the irreversibility of the phase transition in fields up to 8 T due to the wide temperature hysteresis. Additionally, a sharp, more than twofold decrease in the magnitude of the MCE near TC is found with an increase in the cyclic frequency of the magnetic field from 1 to 30 Hz. This behavior is explained by the influence of magnetic and microstructural inhomogeneities, as well as by the lagging of the magnetization behind the magnetic field in alternating magnetic fields (magnetic viscosity). Finally, the specific cooling power for the Ni47Mn40Sn13 alloy is found to increase as the magnetic field frequency increases, with a value of 0.32 W/g at f = 1 Hz and 4.53 W/g at f = 30 Hz.