The interelectronic-interaction corrections of the second order in 1/Z to the ground-state hyperfine splitting in lithiumlike ions are evaluated. The calculations are performed by using the relativistic configuration-interaction method and perturbation theory. In addition, the nuclear magnetization distribution effect on the interelectronic-interaction correction of the first order in 1/Z is evaluated within the single-particle nuclear model. The calculations provide an improvement in the theoretical predictions for the hyperfine splitting in lithiumlike ions.