The purpose of this paper is the study of direct limit in the category of $(m, n)$-ary hypermodules over $(m, n)$-hyperring $R$. In this regards, we introduce and study $R_{(m, n)}-Hmod$, the category of $R_{(m, n)}-Hmod$, and direct limit in this category. In particular, we study a direct limit of morphisms, direct systems of kernels, and cokernels. Finally, we investigate the relationship between the functor home and direct limit and prove that the functor $hom$ preserves direct limit in category $R_{(m, n)}-Hmod$.