Context. As a planet eclipses its parent star, a dark spot on the surface of the star may be occulted, causing a detectable variation in the light curve. Aims: We study these light curve variations during transits and infer the physical characteristics of the stellar spots. Methods: A total of 77 consecutive transit light curves of CoRoT-2 were observed with a high temporal resolution of 32 s, corresponding to an uninterrupted period of 134 days. By analyzing small intensity variations in the transit light curves, it was possible to detect and characterize spots on the surface of the star. The model used simulates planetary transits and enables the inclusion of spots on the stellar surface with different sizes, intensities (i.e., temperatures), and positions. Fitting the data with this model, it is possible to infer the physical characteristics of the spots. Because what is observed is the stellar flux blocked by the spots, there is a degeneracy between the spot intensity and area, although the spot radius defines the shape and width of the signal in the light curve. The model allows up to 9 spots to be present on the stellar surface within the transit band. Results: Before the modeling of the spots was performed, the planetary radius relative to the star radius was estimated by fitting the deepest transit to minimize the effect of spots. A slightly larger (3%) radius, 0.172 Rstar, resulted instead in the previously reported 0.1667 Rstar. The fitting of the transits yields spots, or spot groups, of sizes ranging from 0.2 to 0.7 planetary radius, Rp, with a mean of 0.46 ± 0.11 Rp (~ 100 000 km), resulting in a stellar area covered by spots within the transit latitudes of 10-20%. The intensity varied from 0.3 to 0.8 of the disk center intensity, Ic, with a mean of 0.55 ± 0.13 Ic, which can be converted to temperature by assuming black-body emission for both the photosphere and the spots. Considering an effective temperature of 5625 K for the stellar photosphere, the mean spot temperature is 4700 ± 300 K. Conclusions: The spot model used here was able to estimate the physical characteristics of the spots on CoRoT-2, such as size and intensity. The spots on CoRoT-2 are larger and cooler than sunspots, maybe confirming the more active nature of this star with respect to the Sun. The results presented here are in agreement with those found for magnetic activity analysis from out of transit data of the same star. CoRoT is a space project operated by the French Space Agency, CNES, with participation of the Science Programme of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany, and Spain.