  The Fornax galaxy cluster was observed with the High Energy Stereoscopic
System (H.E.S.S.) for a total live time of 14.5 hours, searching for
very-high-energy (VHE, E>100 GeV) gamma-rays from dark matter (DM)
annihilation. No significant signal was found in searches for point-like and
extended emissions. Using several models of the DM density distribution, upper
limits on the DM velocity-weighted annihilation cross-section <sigma v> as a
function of the DM particle mass are derived. Constraints are derived for
different DM particle models, such as those arising from Kaluza-Klein and
supersymmetric models. Various annihilation final states are considered.
Possible enhancements of the DM annihilation gamma-ray flux, due to DM
substructures of the DM host halo, or from the Sommerfeld effect, are studied.
Additional gamma-ray contributions from internal bremsstrahlung and inverse
Compton radiation are also discussed. For a DM particle mass of 1 TeV, the
exclusion limits at 95% of confidence level reach values of <sigma v> ~
10^-23cm^3s^-1, depending on the DM particle model and halo properties.
Additional contribution from DM substructures can improve the upper limits on
<\sigma v> by more than two orders of magnitude. At masses around 4.5 TeV, the
enhancement by substructures and the Sommerfeld resonance effect results in a
velocity-weighted annihilation cross-section upper limit at the level of
<\sigma v> ~ 10^-26cm^3s^-1.
