Prestressed carbon fibers of at least one textile structure comprising carbon fibers are embedded in a concrete matrix. At least one textile structure comprising carbon fiber bundles is laid in a mold at a distance from one another, into two accommodation elements which are arranged at two diametrical end faces of the mold. Hollow spaces within the accommodation element are filled with a rapid-curing viscous composition having a mineral basis or rapid-curing polymer. After curing the composition or of the polymer, tensile forces act on the accommodation element(s) in the longitudinal direction of the carbon fiber bundles with a tensioning device. During the tensile force the interior of the mold is subsequently filled completely with viscous concrete. After curing of the concrete, the tensile forces on the prestressed carbon fiber bundles are largely transferred to the cured concrete and the concrete component can then be removed from the mold.