Context. Polarimetry is a very powerful tool for uncovering various properties of astronomical objects that otherwise remain hidden in standard imaging or spectroscopic observations. While common observations only measure the intensity of light, polarimetric measurements allow us to distinguish and measure the two perpendicular components of the electric field associated with the incoming light. By using polarimetry it is possible to unveil asymmetries in supernova explosions, properties of intervening dust, characteristics of atmosphere of planets, among others. However, the reliable measurement of the low polarization signal from astronomical sources requires a good control of spurious instrumental polarization induced by the various components of the optical system and the detector. Aims. We perform a detailed multi-wavelength calibration study of the FORS2 instrument at the VLT operating in imaging polarimetric mode to characterize the spatial instrumental polarization that may affect the study of extended sources. Methods. We used imaging polarimetry of high signal-to-noise ratio blank field BVRI observations during the full moon, when the polarization is expected to be constant across the field of view and deviations originate from the instrument, and a crowded star cluster in broad-band RI and narrow-band H_α filters, where the individual polarization values of each star across the field can be measured. Results. We find an instrumental polarization pattern that increases radially outwards from the optical axis of the instrument reaching up to 1.4% at the edges, depending on the filter. Our results are closely approximated by an elliptical paraboloid down to less than ∼0.05% accuracy, and ∼0.02% when using non-analytic fits. We present 2D maps to correct for this spurious instrumental polarization. We also give several tips and tricks for analyzing polarimetric measurements of extended sources. Conclusions. FORS2 is a powerful instrument that allows the linear polarimetry of extended sources to be mapped. We present and discuss a methodology that can be used to measure the polarization of such sources, and to correct for the spatial polarization induced in the optical system. This methodology could be applied to polarimetric measurements using other dual-beam polarimeters.