The widths of the strong decays \(Z_c^{+}(3900)\to J/\psi \pi^{+}\) and \(Z_c^{+}(3900)\to \eta_{c} \rho^{+}\) are calculated. To this end, the mass and decay constant of the exotic \(Z_c^{+}(3900)\) state are computed by means of a two-point sum rule. The obtained results are then used to calculate the strong couplings \(g_{Z_{c}J/\psi \pi }\) and \(g_{Z_{c}\eta_{c} \rho }\) employing QCD sum rules on the light-cone supplied by a technique of the soft-meson approximation. We compare our predictions on the mass and decay widths with available experimental data and other theoretical results.