We report on high-energy properties of the black widow pulsar PSR J2241$-$5236 in the X-ray and the Fermi-LAT (GeV gamma-ray) bands. In the LAT band, the phase-averaged gamma-ray light curve shows orbital modulation below $sim$1 GeV with a chance probability ($p$) monotonically decreasing with time to $psim 10^{-5}$. The peak of the light curve is near the superior conjunction of the pulsar (binary phase $phi_{rm B}approx 0.25$). We attribute the modulation to the intra-binary shock (IBS) emission and search for IBS signatures in the archival X-ray data. We find that the X-ray spectral fit requires a non-thermal component, which implies a possible IBS origin of the X-rays. We discuss our observations in the context of IBS scenarios.