Exciton states have been studied experimentally in strained ZnSe/(Zn,Mg)Se quantum well structures with a Mg content of only 3.6% by means of magnetoreflectivity and ultrafast piezospectroscopy. The small intrinsic band gap difference and the built-in strain in barriers and quantum wells lead to a shallow confinement potential for heavy holes which is smaller than the Coulomb electron-hole interaction. An exciton state formed by a confined electron and heavy-hole continuum states is identified. The experimental findings are supported by numerical model calculations.