  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 $p\sim 10^{-5}$. 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.
