Isotope shifts of n = 1 and n= 2 levels and corresponding transitions in helium-like highly charged ions are calculated with high precision. The total value of the isotope shift is determined mainly by the sum of the field and mass shifts. The field shift is calculated by using the Dirac-Fock-Sturm method taking into account interaction of configurations. Quantum-electrodynamic corrections to this contribution are taken into account approximately by using the corresponding one-electron expressions. The mass shift is calculated both within the framework of the Breit approximation and by taking into account quantum-electrodynamic contributions that become substantial for heavy ions. In the case of thorium and uranium ions, corrections due to nuclear polarization and deformation are taken into account additionally.