Classical Be stars are rapidly rotating stars with circumstellar disks that come and go on time scale of years. Recent observational data strongly suggests that these stars lack the 10% incidence of global magnetic fields observed in other main-sequence B stars. Such an apparent lack of magnetic fields may indicate that Be disks are fundamentally incompatible with a significant large scale magnetic field. In this work, using numerical magnetohydrodynamics (MHD) simulations, we show that a dipole field of only 100G can lead to the quick disruption of a Be disk. Such a limit is in line with the observational upper limits for these objects.