Context : The CoRoT satellite has recently discovered a hot Jupiter that transits across the disc of a F9 main-sequence star called CoRoT-6 with a period of 8.886 days .

Aims : We model the photospheric activity of the star and use the maps of the active regions to study stellar differential rotation and the star-planet interaction .

Methods : We apply a maximum entropy spot model to fit the optical modulation as observed by CoRoT during a uninterrupted interval of \sim 140 days .
Photospheric active regions are assumed to consist of spots and faculae in a fixed proportion with solar-like contrasts .

Results : Individual active regions have lifetimes up to 30 - 40 days .
Most of them form and decay within five active longitudes whose different migration rates are attributed to the stellar differential rotation for which a lower limit of \Delta \Omega / \Omega = 0.12 \pm 0.02 is obtained .
Several active regions show a maximum of activity at a longitude lagging the subplanetary point by \sim 200 ^ { \circ } with the probability of a chance occurrence being smaller than 1 percent .

Conclusions : Our spot modelling indicates that the photospheric activity of CoRoT-6 could be partially modulated by some kind of star-planet magnetic interaction , while an interaction related to tides is highly unlikely because of the weakness of the tidal force .