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Surface magnetic fields are routinely measured in stars. However, internal magnetic fields are inaccessible to direct observations and very little is known about their amplitude, geometry and evolution. In this paper, we demonstrate that strong magnetic fields in the cores of red giant stars can suppress the amplitudes of dipolar oscillation modes. The suppression arises from a magnetic greenhouse effect that causes incoming wave energy to be trapped within the core. Suppressed dipolar modes are indeed observed in a significant fraction of {\it Kepler} red giant stars. We interpret these as stars with strongly magnetized cores, and we place lower limits on their internal magnetic field strength. The inferred field strengths fields  indicate these stars are the descendants of magnetic Ap stars or hosted a powerful core dynamo during the main sequence. The novel asteroseismic technique reported here allows for constraints on magnetic fields in the deep interiors of a large population of stars.