The rigorous quantum electrodynamic approach is applied for the derivation of the Stark shift of the atomic energy levels induced by blackbody radiation (BBR) within the framework of perturbation theory. The temperature-dependent one-loop self-energy (SE) correction of bound atomic electron states accounting for the number of photons represented by the Planckian frequency-distribution function is examined. According to this approach, the energy shift arises as the real part of self-energy correction while the imaginary part describes the BBR-induced depopulation rate for a given atomic state. Moreover, regularization of the divergent energy denominators arising in the SE correction leads to an additional correction to the level width that has not been considered before and can be explained by the mixing effect of atomic levels in the presence of the BBR-induced mean electric field.