We present wide-field g- and i-band stellar photometry of the Sextans dwarf spheroidal galaxy and its surrounding area out to four times its half-light radius (r_h_=695pc), based on images obtained with the Dark Energy Camera at the 4-m Blanco telescope at CTIO. We find clear evidence of stellar substructure associated with the galaxy, extending to a distance of 82-arcmin (2kpc) from its centre. We perform a statistical analysis of the overdensities and find three distinct features, as well as an extended halo-like structure, to be significant at the 99.7 per cent confidence level or higher. Unlike the extremely elongated and extended substructures surrounding the Hercules dwarf spheroidal galaxy, the overdensities seen around Sextans are distributed evenly about its centre, and do not appear to form noticeable tidal tails. Fitting a King model to the radial distribution of Sextans stars yields a tidal radius r_t_=83.2-arcmin+/-7.1 arcmin (2.08+/-0.18kpc), which implies the majority of detected substructure is gravitationally bound to the galaxy. This finding suggests that Sextans is not undergoing significant tidal disruption from the Milky Way, supporting the scenario in which the orbit of Sextans has a low eccentricity.