Context. Since the launch of the Fermi satellite, the number of known gamma-ray pulsars has increased tenfold. Most gamma-ray detected pulsars are young and energetic, and many are associated with TeV sources. PSR J1357−6429 is a high spin-down power pulsar (Ė = 3.1 × 1036 erg s-1), discovered during the Parkes multibeam survey of the Galactic plane, with significant timing noise typical of very young pulsars. In the very-high-energy domain (E > 100 GeV), H.E.S.S. has reported the detection of the extended source HESS J1356−645 (intrinsic Gaussian width of 12′) whose centroid lies 7′ from PSR J1357−6429. Aims. We search for gamma- and X-ray pulsations from this pulsar, characterize the neutron star emission and explore the environment of PSR J1357−6429. Methods. Using a rotational ephemeris obtained with 74 observations made with the Parkes telescope at 1.4 GHz, we phase-fold more than two years of gamma-ray data acquired by the Large Area Telescope on-board Fermi as well as those collected with XMM-Newton, and perform gamma-ray spectral modeling. Results. Significant gamma- and X-ray pulsations are detected from PSR J1357−6429. The light curve in both bands shows one broad peak. Gamma-ray spectral analysis of the pulsed emission suggests that it is well described by a simple power-law of index 1.5 ± 0.3stat ± 0.3syst with an exponential cut-off at 0.8 ± 0.3stat ± 0.3syst GeV and an integral photon flux above 100 MeV of (6.5 ± 1.6stat ± 2.3syst)    ×    10-8 cm-2 s-1. The X-ray spectra obtained from the new data provide results consistent with previous work. Upper limits on the gamma-ray emission from its potential pulsar wind nebula (PWN) are also reported. Conclusions. Assuming a distance of 2.4 kpc, the Fermi LAT energy flux yields a gamma-ray luminosity for PSR J1357−6429 of Lγ = (2.13 ± 0.25stat ± 0.83syst) × 1034 erg s-1, consistent with an \hbox{$L_\gamma \propto \sqrt{\dot E}$}Lγ∝Ė relationship. The Fermi non-detection of the pulsar wind nebula associated with HESS J1356−645 provides new constraints on the electron population responsible for the extended TeV emission.