Atmospheric Cherenkov telescopes rely on the Earth's atmosphere as part of the detector. The presence of clouds affects observations and can introduce biases if not corrected for. Correction methods typically require an atmospheric profile, that can be measured with external atmospheric monitoring devices. We present a novel method for measuring the atmospheric profile using the data from Imaging Atmospheric Cherenkov telescopes directly. The method exploits the comparison of average longitudinal distributions of the registered Cherenkov light between clear atmosphere and cloud presence cases. Using Monte Carlo simulations of a subarray of four Large-Sized Telescopes of the upcoming Cherenkov Telescope Array Observatory and a simple cloud model we evaluate the accuracy of the method in determining the basic cloud parameters. We find that the method can reconstruct the transmission of typical clouds with an absolute accuracy of a few per cent. For low-zenith observations, the height of the cloud centre can be reconstructed with a typical accuracy of a few hundred metres, while the geometrical thickness can be accurately reconstructed only if it is ≳3 km. We also evaluate the robustness of the method against the typical systematic uncertainties affecting atmospheric Cherenkov telescopes. •A novel method is proposed for the evaluation of cloud transmission profile using Cherenkov telescope data.•The method provides total transmission measurement with absolute accuracy of a few per cent.•The cloud height is reconstructed with a small bias, while the cloud thickness can be reconstructed well only if ≳3 km.•The method can serve as an auxiliary cloud parameters measurement without additional hardware or loss of observation time.