In this work, a non-destructive, automated procedure to extract the I-V characteristics of individual cells of fully encapsulated photovoltaic (PV) modules is proposed. The approach is able to correctly identify and extract the electrical parameters of underperforming cells, due for example to defects or degradation. The approach uses multiple I-V measurements on the PV module assuming specific levels of shading on the individual cells. The single circuit models for the cells are obtained through the solution of an inverse fitting problem. The approach was validated in a simulated environment through statistical analysis, with the cell parameters based on real silicon PV devices. The computational complexity of the approach is also investigated and validation examples with different configurations of PV modules, including bypass diodes are presented. The approach was validated on several tests to assess noise robustness, flexibility in terms of cells non-uniformities and scalability towards larger systems, resulting in a lean and accurate procedure for I-V curves extraction. The proposed methodology can be potentially utilised for automated quality assurance and fault assessment of PV modules, investigation of degradation mechanisms of cells in PV modules, or quantitative validation of other optical imaging techniques such as luminescence imaging and infrared thermography.