Tool for machining a workpiece having a cutting insert with at least one cutting edge. Moreover, the tool has a tool holder, which extends along a holder longitudinal axis and has at a workpiece-side end a cutting insert receptacle for receiving the cutting insert, the cutting insert receptacle having an upper clamping finger and a lower clamping jaw. Furthermore, the tool has a wedge-shaped clamping element, which is fastenable in the cutting insert receptacle for wedging the cutting insert in the tool holder. In addition, the tool comprises a fastening element for fastening the clamping element in the cutting insert receptacle and for wedging the cutting insert in the tool holder.