An optoelectronic semiconductor component and a method for making an optoelectronic semiconductor component are disclosed. In an embodiment the component includes a carrier including at least one conversion-medium body and a potting body, the potting body surrounding the conversion-medium body at least in places, as seen in plan view, electrical contact structures fitted at least indirectly to the carrier and a plurality of optoelectronic semiconductor chips fitted to a main face of the carrier, the optoelectronic semiconductor chips configured to generate radiation, wherein the conversion-medium body is shaped as a plate, wherein the semiconductor chips are directly mechanically connected to the conversion-medium body, and wherein the conversion-medium body is free of cutouts for the electrical contact structures and is not penetrated by the electrical contact structure.