A method is disclosed for the manufacture of an optoelectronic component. A substrate has a first primary face and a second primary face that lies opposite the first primary face. A semiconductor body that is capable of emitting electromagnetic radiation from a front side is attached to the first primary face of the substrate. A covering that is transparent to the radiation from the optoelectronic semiconductor body is applied to at least the front side of the semiconductor body. The covering is given the form of an optical element by using a closed cavity that is shaped with the contour of the optical element.