The Higgs-fermion couplings are sensitive probes of possible new physics behind a stable light Higgs particle. It is then essential to identify the flavor pattern of those interactions. We consider the case in which a strong dynamics lies behind a light Higgs and explore the implications within the minimal flavor violation ansatz. The dominant effects on flavor-changing Higgs-fermion couplings stem in this context from operators with mass dimension $\ensuremath{\le}5$, and we analyze all relevant chiral operators up to that order, including loop corrections induced by four-dimensional ones. Bounds on the operator coefficients are derived from a plethora of low-energy flavor transitions, providing a guideline on which flavor-changing Higgs interactions may be open to experimental scrutiny. In particular, the coefficient of a genuinely $CP$-odd operator is only softly constrained and therefore its impact is potentially interesting.