Solvent effects on the nuclear shielding and indirect spin-spin coupling constants of H2Se have been calculated by modeling the surroundings as a continuous dielectric medium. Gauge-origin independence of the nuclear shieldings is ensured by using London atomic orbitals in combination with linear response theory. We present the Linear response function of a solvated molecule subject to triplet perturbations and use a new implementation of this theory to evaluate the Fermi-contact and spin-dipole contributions to the indirect spin-spin coupling constants, We present high-level calculations of the nuclear shielding and indirect spin-spin coupling constants of H2Se in vacuum and different solvents. Our results represent the first ab initio calculations of the spin-spin coupling constants in H2Se as well as the first investigation of medium effects on these properties. It is demonstrated that the solvent shifts of the spin-spin couplings are caused by a polarization of the molecular electronic structure as well as by changes in the geometry upon solvation.