A generic expression of double-parton scattering cross sections in high-energy nucleus-nucleus (A-A) collisions is derived as a function of the corresponding single-parton hard cross sections and of the A-A event centrality. We consider the case of prompt-J/psi production in lead-lead (Pb-Pb) at the CERN Large Hadron Collider and find that about 20% (35%) of the J/psi events in minimum-bias (most central) collisions contain a second J/psi from double parton interactions. In Pb-Pb at 5.5 TeV, in the absence of final-state effects, about 240 double-J/psi events are expected per unit midrapidity and per inverse-nanobarn in the dilepton decay modes. The implications of double-J/psi production on the interpretation of the observed J/psi suppression in A-A collisions are discussed.