Relativistic calculations of the isotope shifts of energy levels in highly charged Li-like ions are performed. The nuclear recoil (mass shift) contributions are calculated by merging the perturbative and large-scale configuration- interaction Dirac-Fock-Sturm (CI-DFS) methods. The nuclear size (field shift) contributions are evaluated by the CI-DFS method including the electron-correlation, Breit, and QED corrections. The nuclear deformation and nuclear polarization corrections to the isotope shifts in Li-like neodymium, thorium, and uranium are also considered. The results of the calculations are compared with the theoretical values obtained with other methods.