One of the remarkable properties of the II-VI diluted magnetic semiconductor (ZnMn)Se is the giant spin splitting of the valence-band states under application of the magnetic field (giant Zeeman splitting). This splitting reveals strong exchange interaction between Mn moments and semiconductor states. On the other hand, no magnetic phase transition has been observed for systems with small Mn content up to very low temperatures. The latter property shows weakness of the exchange interaction between Mn moments. In this paper, the local-density approximation (LDA) and the LDA+U techniques are employed to study exchange interactions in (ZnMn)Se. Supercell and frozen-magnon approaches applied earlier to III-V diluted magnetic semiconductors are used. It is found that both LDA and LDA+U describe successfully the combination of the strong Zeeman splitting and weak-interatomic exchange. However, the physical pictures provided by two techniques differ strongly. A detailed analysis shows that the LDA+U method provides the description of the system which is much closer to the experimental data.