We study the decay of the lightest neutral Higgs boson to a charm quark pair at full one-loop level in the MSSM with non-minimal quark flavour violation (QFV). In the numerical analysis we consider mixing between the second and the third squark generation and all relevant constraints from B meson data are taken into account. It is shown that the full one-loop corrected decay width can be quite sensitive to the MSSM QFV parameters due to large $tilde c - tilde t$ mixing and large trilinear couplings. After summarising the theoretical and experimental errors, we conclude that an observation of these SUSY QFV effects is possible at the ILC.