In the indirect dark matter (DM) detection framework, the DM particles would produce some signals by self-annihilating and creating standard model products such as γ rays, which might be detected by ground-based telescopes. Dwarf irregular galaxies represent promising targets for the search for DM as they are assumed to be dark matter dominated systems at all radii. These dwarf irregular galaxies are rotationally supported with relatively simple kinematics which lead to small uncertainties on their dark matter distribution profiles. In 2018, the H.E.S.S. telescopes observed the irregular dwarf galaxy Wolf-Lundmark-Melotte (WLM) for a live time of 19 hours. These observations are the very first ones made by an imaging atmospheric Cherenkov telescope toward this kind of object. We search for a DM signal looking for an excess of γ rays over the background in the direction of the WLM galaxy. We present the first results obtained on the velocity weighted cross section for DM self-annihilation as a function of DM particle mass.