Let \(U_q(\mathfrak g)\) be the quantum loop algebra associated to an affine Kac-Moody algebra \(\mathfrak g\) of untwisted type. D. Hernandez and M. Jimbo introduced in [Compos. Math. 148, No. 5, 1593–1623 (2012; Zbl 1266.17010)] a certain category \(\mathcal O\) of \(U_q(\mathfrak b)\)-modules, where \(\mathfrak b\) is the Borel subalgebra of \(\mathfrak g\), which contains the finite-dimensional \(U_q(\mathfrak g)\)-modules, and considered, for every non-zero \(a \in \mathbb C(q)\) and \(r\) in the index set \(I=\{1, \dots, n\}\) of the Dynkin diagram, the prefundamental representations \(L^{\pm}_{r,a}\), which are relevant to the study of the category \(\mathcal O\). The main result of the paper under review is an explicit realization of \(L^{\pm}_{r,a}\) when \(\mathfrak g = A_n^{(1)}, D_n^{(1)}\) and \(r \in I\) is minuscule.