We present a study of the light curve of the transiting exoplanet CoRoT-2b, aimed at detecting the secondary eclipse and measuring its depth. The data were obtained with the CoRoT satellite during its first run of more than 140 days. After filtering the low frequencies with a pre-whitening technique, we detect a 0.0060±0.0020% secondary eclipse centered on the orbital phase 0.494± 0.006. Assuming a black-body emission of the planet, we estimate a surface brightness temperature of T_p,CoRoT =1910+90-100 K. We provide the planet's equilibrium temperature and re-distribution factors as a function of the unknown amount of reflected light. The upper limit for the geometric albedo is 0.12. The detected secondary is the shallowest ever found. Based on observations obtained with CoRoT, a space project operated by the French Space Agency, CNES, with participation of the Science Program of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany, and Spain.