We investigate laser-induced torques in magnetically non-collinear ferromagnets with a spin-spiral magnetic structure using textit{ab-initio} calculations. Since spin-spirals may be used to approximate the magnetization gradients locally in domain walls and skyrmions, our method may be used to obtain the laser-induced torques in such objects from a multiscale approach. Employing the generalized Bloch-theorem we obtain the electronic structure computationally efficiently. We employ our method to assess the laser-induced torques in bcc Fe, hcp Co, and L$_{1}0$ FePt when a spin-spiral magnetic structure is imposed. We find that the laser-induced torques in these magnetically noncollinear systems may be orders of magnitude larger than those in the corresponding magnetically collinear systems and that they exist both for linearly and circularly polarized light. This result suggests that laser-induced torques driven by noncollinear magnetic order or by magnetic fluctuations may contribute significantly to processes in ultrafast magnetism.