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Space-based asteroseismology has opened a window into the interiors of red giants. Mixed modes have made it possible to distinguish between hydrogen- and helium-burning red giants \cite{Bedding_2011}. The rotational splitting of mixed modes has been used to determine the degree of differential rotation in red giants interiors, revealing that the cores of red giant stars rotate much faster than their envelopes \cite{Beck_2011}, but much slower than predicted by theory \cite{Cantiello_2014}.   The amplitudes of solar-like oscillations in red giant branch (RGB) stars depends on the interplay between driving and damping of the modes \citet{Dupret_2009}. Interestingly, a family of red giants with very weak dipole modes has been identified by \citet{Mosser_2011}. \citet{Mosser_2011} (see Figure \ref{fig:moneyplot}).  These stars have normal radial pulsation modes (harmonic degree $\ell=0$) , but exhibit depressed dipolar ($\ell=1$) modes. Here, we demonstrate that the presence of a strongly magnetized core suppresses the visibility of dipolar modes via a ``magnetic greenhouse" effect. We show that magnetic suppression reduces the visibility of dipole modes to the level observed by \citet{Mosser_2011} in suppressed dipolar pulsators, suggesting these stars host strong magnetic fields in their cores. We develop a novel asteroseismic technique that places tight constraints on (and in some cases yields measurements of) the magnetic fields in red giant cores.