  Aims: Following the detection of the fast radio burst FRB150418 by the SUPERB
project at the Parkes radio telescope, we aim to search for very-high energy
gamma-ray afterglow emission. Methods: Follow-up observations in the very-high
energy gamma-ray domain were obtained with the H.E.S.S. imaging atmospheric
Cherenkov telescope system within 14.5 hours of the radio burst. Results: The
obtained 1.4 hours of gamma-ray observations are presented and discussed. At
the 99 % C.L. we obtained an integral upper limit on the gamma-ray flux of
(E>350 GeV) < 1.33 x 10^-8 m^-2s^-1. Differential flux upper limits as function
of the photon energy were derived and used to constrain the intrinsic
high-energy afterglow emission of FRB 150418. Conclusions: No hints for
high-energy afterglow emission of FRB 150418 were found. Taking absorption on
the extragalactic background light into account and assuming a distance of z =
0.492 based on radio and optical counterpart studies and consistent with the
FRB dispersion, we constrain the gamma-ray luminosity at 1 TeV to L < 5.1 x
10^47 erg/s at 99% C.L.

High Energy Astrophysical Phenomena