Context : Type Ic supernovae ( SNe Ic ) arise from the core-collapse of H ( and He ) poor stars , which could be either single WR stars or lower-mass stars stripped of their envelope by a companion . Their light curves are radioactively powered and usually show a fast rise to peak ( \sim 10 - 15 d ) , without any early ( first few days ) emission bumps ( with the exception of broad-lined SNe Ic ) as sometimes seen for other types of stripped-envelope SNe ( e.g. , Type IIb SN 1993J and Type Ib SN 2008D ) . Aims : We have studied iPTF15dtg , a spectroscopically normal SN Ic with an early excess in the optical light curves followed by a long ( \sim 30 d ) rise to the main peak . It is the first spectroscopically-normal double-peaked SN Ic observed . We aim to determine the properties of this explosion and of its progenitor star . Methods : Optical photometry and spectroscopy of iPTF15dtg was obtained with multiple telescopes . The resulting light curves and spectral sequence are analyzed and modelled with hydrodynamical and analytical models , with particular focus on the early emission . Results : iPTF15dtg is a slow rising SN Ic , similar to SN 2011bm . Hydrodynamical modelling of the bolometric properties reveals a large ejecta mass ( \sim 10 M _ { \odot } ) and strong ^ { 56 } Ni mixing . The luminous early emission can be reproduced if we account for the presence of an extended ( \gtrsim 500 R _ { \odot } ) , low-mass ( \gtrsim 0.045 M _ { \odot } ) envelope around the progenitor star . Alternative scenarios for the early peak , such as the interaction with a companion , a shock-breakout ( SBO ) cooling tail from the progenitor surface , or a magnetar-driven SBO are not favored . Conclusions : The large ejecta mass and the presence of H and He free extended material around the star suggest that the progenitor of iPTF15dtg was a massive ( \gtrsim 35 M _ { \odot } ) WR star suffering strong mass loss .