We investigate the impact of modified-gravity models on the Lyman-α power spectrum. Building a simple analytical modeling, based on a truncated Zeldovich approximation, we estimate the intergalactic medium power spectrum and the Lyman-α flux decrement power spectrum along the line of sight. We recover the results of numerical simulations for f (R)-gravity models and present new results for K-mouflage scenarios. We find that the shape of the distortion due to the modified gravity depends on the model, through the scaledependence or not of their growth rate. This is more clearly seen in the three-dimensional power spectrum than in the one-dimensional power spectrum, where the line-of-sight integration smoothes the deviation. Whilst the Lyman-α power spectrum does not provide competitive bounds for f (R) theories, it could provide useful constraints for the K-mouflage models. Thus, the efficiency of the Lyman-α power spectrum as a probe of modified-gravity scenarios depends on the type of screening mechanism and the related scale dependence it induces. The prospect of a full recovery of the three-dimensional Lyman-α power spectrum from data would also lead to stronger constraints and a better understanding of screening mechanisms.