Let $\mathfrak{a}$ be an ideal of a commutative Noetherian ring $R$ and $M, N$ be two finitely generated $R$-modules. Let $t$ be a non-negative integer. It is shown that if the local cohomology module $H_{\mathfrak{a}}^i(N)$ is minimax for all $i < t$, then the generalized local cohomology module $H_{\mathfrak{a}}^i(M, N)$ is minimax for all $i < t$. Also, we prove that if the generalized local cohomology module $H^i_{\mathfrak{a}}(M, N)$ is minimax for all i $< t$, then for any minimax module $L$ the $R$-module $\mathrm{Hom}_R(R/\mathfrak{a}, H_{\mathfrak{a}}^t(M, N)/L)$ is finitely generated. In particular, $\mathrm{Ass}_R(H_{\mathfrak{a}}^t(M, N)/L)$ is a finite set.