<p>This paper is devoted to the study of approximate solutions for a class of multiobjective interval-valued optimization problems based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some mild conditions. Moreover, we give KKT optimality conditions of approximate solutions for such a problem whose associated functions are nonsmooth and nonconvex. We also propose the approximate KKT optimality condition of an approximate solution for such a problem. Finally, we apply some obtained results to a noncooperative game involving the multiobjective interval-valued nonsmooth function and to a multiobjective interval-valued variational problem.</p>