To explore non-adiabatic effects caused by electromagnetic (EM) vacuum fluctuations in molecules, we develop a general theory of internal conversion (IC) in the framework of quantum electrodynamics and propose a new mechanism, "quantum electrodynamic internal conversion" (QED-IC). The theory allows us to compute the rates of the conventional IC and QED-IC processes at the first-principles level. Our simulations manifest that, under experimentally feasible weak light-matter coupling conditions, EM vacuum fluctuations can significantly affect IC rates by an order of magnitude. Moreover, our theory elucidates three key factors in the QED-IC mechanism: the effective mode volume, coupling-weighted normal mode alignment, and molecular rigidity. The theory successfully captures the nucleus-photon interaction in the factor "coupling-weighted normal mode alignment". In addition, we find that molecular rigidity plays a totally different role in conventional IC versus QED-IC rates. Our study provides applicable design principles for exploiting QED effects on IC processes.