Context. The CoRoT satellite has recently discovered the transits of an Earth-like planet across the disc of a late-type magnetically active star dubbed CoRoT-7, while a second planet was detected after filtering out the radial velocity (hereafter RV) variations due to stellar activity. Aims: We investigate the magnetic activity of CoRoT-7 and use the results for a better understanding of the impact of magnetic activity on stellar RV variations. Methods: We derived the longitudinal distribution of active regions on CoRoT-7 from a maximum entropy spot model of the CoRoT lightcurve. Assuming that each active region consists of dark spots and bright faculae in a fixed proportion, we synthesized the expected RV variations. Results: Active regions are mainly located at three active longitudes that appear to migrate at different rates, probably as a consequence of surface differential rotation, for which a lower limit of ΔΩ/Ω = 0.058 ± 0.017 is found. The synthesized activity-induced RV variations reproduce the amplitude of the observed RV curve and are used to study the impact of stellar activity on planetary detection. Conclusions: In spite of the non-simultaneous CoRoT and HARPS observations, our study confirms the validity of the method previously adopted to filter out RV variations induced by stellar activity. We find a false-alarm probability <10-4 that the RV oscillations attributed to CoRoT-7b and CoRoT-7c are spurious effects of noise and activity. Additionally, our model suggests that other periodicities found in the observed RV curve of CoRoT-7 could be explained by active regions whose visibility is modulated by a differential stellar rotation with periods ranging from 23.6 to 27.6 days. Based on observations obtained with CoRoT, a space project operated by the French Space Agency, CNES, with partecipation of the Science Programme of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany, and Spain.