Aims. The SHINE program is a high-contrast near-infrared survey of 600 young, nearby stars aimed at searching for and characterizing new planetary systems using VLT/SPHERE’s unprecedented high-contrast and high-angular-resolution imaging capabilities. It is also intended to place statistical constraints on the rate, mass and orbital distributions of the giant planet population at large orbits as a function of the stellar host mass and age to test planet-formation theories. Methods. We used the IRDIS dual-band imager and the IFS integral field spectrograph of SPHERE to acquire high-contrast coronagraphic differential near-infrared images and spectra of the young A2 star HIP 65426. It is a member of the ~17 Myr old Lower Centaurus-Crux association. Results. At a separation of 830 mas (92 au projected) from the star, we detect a faint red companion. Multi-epoch observations confirm that it shares common proper motion with HIP 65426. Spectro-photometric measurements extracted with IFS and IRDIS between 0.95 and 2.2 μm indicate a warm, dusty atmosphere characteristic of young low-surface-gravity L5-L7 dwarfs. Hot-start evolutionary models predict a luminosity consistent with a 6–12 MJup, Teff = 1300–1600 K and R = 1.5 ± 0.1 RJup giant planet. Finally, the comparison with Exo-REM and PHOENIX BT-Settl synthetic atmosphere models gives consistent effective temperatures but with slightly higher surface gravity solutions of log (g) = 4.0–5.0 with smaller radii (1.0–1.3 RJup). Conclusions. Given its physical and spectral properties, HIP 65426 b occupies a rather unique placement in terms of age, mass, and spectral-type among the currently known imaged planets. It represents a particularly interesting case to study the presence of clouds as a function of particle size, composition, and location in the atmosphere, to search for signatures of non-equilibrium chemistry, and finally to test the theory of planet formation and evolution.