A semiconductor module includes a printed circuit board, a ceramic substrate and a semiconductor chip. The printed circuit board includes an insulating material, a cutout formed in the insulating material, and a first metallization layer, which is partly embedded into the insulating material. The first metallization layer includes a conductor track projection projecting into the cutout. The ceramic substrate includes a dielectric, ceramic insulation carrier, and an upper substrate metallization applied to a top side of the insulation carrier. The semiconductor chip is arranged on the upper substrate metallization, and the first metallization layer is mechanically and electrically conductively connected to the upper substrate metallization at the conductor track projection.