Zero-index metamaterials (ZIMs) feature a uniform electromagnetic mode over a large area in arbitrary shapes, enabling many applications including high-transmission supercouplers with arbitrary shapes, direction-independent phase matching for nonlinear optics, and collective emission of many quantum emitters. However, most ZIMs reported to date are passive; active ZIMs that allow for dynamic modulation of their electromagnetic properties have rarely been reported. Here, we design and fabricate a magnetically tunable ZIM consisting of yttrium iron garnet (YIG) pillars sandwiched between two copper clad laminates in the microwave regime. By harnessing the Cotton–Mouton effect of YIG, the metamaterial was successfully toggled between gapless and bandgap states, leading to a “phase transition” between a zero-index phase and a single negative phase of the metamaterial. Using an S-shaped ZIM supercoupler, we experimentally demonstrated a tunable supercoupling state with a low intrinsic loss of 0.95 dB and a high extinction ratio of up to 30.63 dB at 9 GHz. We have also engineered a transition between the supercoupling state and the topological one-way transmission state at 10.6 GHz. Our work enables dynamic modulation of the electromagnetic characteristics of ZIMs, enabling various applications in tunable linear, nonlinear, quantum, and nonreciprocal electromagnetic devices.