The interaction between electronic and nuclear degrees of freedom in single-molecule junctions is an essential mechanism, which may result in the current-induced rupture of chemical bonds. As such, it is fundamental for the stability of molecular junctions and for the applicability of molecular electronic devices. In this publication, we study current-induced bond rupture in molecular junctions using a numerically exact scheme, which is based on the hierarchical quantum master equation (HQME) method in combination with a discrete variable representation for the nuclear degrees of freedom. Employing generic models for molecular junctions with dissociative nuclear potentials, we identify distinct mechanisms leading to dissociation, namely, the electronic population of antibonding electronic states and the current-induced heating of vibrational modes. Our results reveal that the latter plays a negligible role whenever the electronic population of antibonding states is energetically possible. Consequently, the significance of current-induced heating as a source for dissociation in molecular junctions involving an active antibonding state is restricted to the nonresonant transport regime, which reframes the predominant paradigm in the field of molecular electronics.