We show that strongly coupled field theories with holographic gravity duals at finite charge density and low temperatures can undergo de Haas-van Alphen quantum oscillations as a function of an external magnetic field. Exhibiting this effect requires computation of the one-loop contribution of charged bulk fermions to the free energy. The one-loop calculation is performed using a formula expressing determinants in black hole backgrounds as sums over quasinormal modes. At zero temperature, the periodic nonanalyticities in the magnetic susceptibility as a function of the inverse magnetic field depend on the low energy scaling behavior of fermionic operators in the field theory, and are found to be softer than in weakly coupled theories. We also obtain numerical and WKB results for the quasinormal modes of charged bosons in dyonic black hole backgrounds, finding evidence for nontrivial periodic behavior as a function of the magnetic field.