Context. The second short run (SRa02) of the CoRoT space mission for asteroseismology was partly devoted to stars belonging to the Mon OB2 association. An intense monitoring has been performed on Plaskett's star (HD 47129) and the unprecedented quality of the light curve allows us to shed new light on this very massive, non-eclipsing binary system. Aims: We particularly aimed at detecting periodic variability that might be associated with pulsations or interactions between both components. We also searched for variations related to the orbital cycle that could help to constrain the inclination and the morphology of the binary system. Methods: We applied an iterative Fourier-based prewhitening and a multiperiodic fitting procedure to analyse the time series and extract the frequencies of variations from the CoRoT light curve. We describe the noise properties to tentatively define an appropriate significance criterion and, in consequence, to only point out the peaks at a certain significance level. We also detect the variations related to the orbital motion and study them with the NIGHTFALL programme. Results: The periodogram computed from Plaskett's star CoRoT light curve mainly exhibits a majority of peaks at low frequencies. Among these peaks, we highlight a list of 43 values, notably including two different sets of harmonic frequencies whose fundamental peaks are located at about 0.07 and 0.82 d-1. The former represents the orbital frequency of the binary system, whilst the latter could probably be associated with non-radial pulsations. The study of the 0.07 d-1 variations reveals a hot spot most probably situated on the primary star and facing the secondary. Conclusions: The investigation of this unique dataset constitutes a further step in the understanding of Plaskett's star. These results provide a first basis for future seismic modelling and put forward the probable existence of non-radial pulsations in Plaskett's star. Moreover, the fit of the orbital variations confirms the problem of the distance of this system which was already mentioned in previous works. A hot region between both components renders the determination of the inclination ambiguous. The CoRoT space mission was developed and is operated by the French space agency CNES, with participation of ESA's RSSD and Science Programmes, Austria, Belgium, Brazil, Germany and Spain.Table 2 is only available in electronic form at http://www.aanda.org