A ligand specific to a bioactive substance to be purified is fixed, via a connecting silane, to a mineral particulate carrier chosen from among SiO.sub.2, Al.sub.2 O.sub.3, ZrO.sub.2 and TiO.sub.2, the particles of the carrier being submicronic, non-porous and having a large specific surface. The carrier is contacted with an aqueous extract containing inter alia the bioactive substances, for the time required for the substance to become specifically fixed to the carrier. The carrier is then separated and the desired bioactive substance is isolated by desorption.