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Internal stellar magnetic fields are inaccessible to direct observations and little is known about their amplitude, geometry and evolution. Here, we demonstrate that strong magnetic fields in the cores of red giant stars can suppress dipole oscillation modes. The suppression arises from a magnetic greenhouse effect causing incoming wave energy to be trapped within the core. Suppressed dipole modes are indeed observed in roughly $20 \%$ of lower young  red giants, and we interpret these as stars with magnetized cores. We place lower limits on the core field strengths, which indicate these stars have retained fossil fields or hosted a core dynamo during the main sequence. The novel technique reported here allows for constraints on magnetic fields in the deep interiors of large populations of stars.