The problem of the binding energy of an exciton R^ex formed by carriers from certain spin subbands has been solved for hexagonal diluted magnetic semiconductors (DMS) with the energy bands spin-split by the exchange field G. It has been shown that in the case of H//c₆ (H is the external magnetic field, c₆ is an axis of the sixth order) the field G//H can affect considerably the effective masses only in the hole B and C subbands (the influences are different for various spin states), while the effective masses are changed in all the whole subbands when H perpendicular to c₆. As a result, dependences of R^ex on G arise and lead, in certain cases, to considerable changes in the band splittings of the exciton transition spectra. Quantitative estimations of the effect were carried out for DBS band parameters corresponding to Cd_1-xMn_xS and Cd_1-xMn_xSe.