The present article is devoted to multitime multiobjective variational problems via $\eta$-approximation method. In this method, an $\eta$-approximation approach is applied to the considered problem, and a new problem is constructed, called as $\eta$-approximated multitime multiobjective variational problem that contains the change in objective and both constraints functions. The equivalence between an efficient (Pareto optimal) solution to the main multitime multiobjective variational problem is derived along with its associated $\eta$-approximated problem under invexity defined for a multitime functional. Furthermore, we have also discussed the saddle-point criteria for the problem considered and its associated $\eta$-approximated problems via generalized invexity assumptions.