We investigate departures from the Hamiltonian dynamics such as the quantum decoherence in superpartner quantum systems due to their interaction with the environment. The effective description is given by the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. The prescription for supersymmetrization of this equation is elaborated upon and pairs of related isospectral quantum systems are built. We present some instructive examples of such a construction.