Melt spinning of a novel piezoelectric bicomponent fiber, with poly(vinylidene fluoride) as the electroactive sheath component, has been demonstrated. An electrically conductive compound of carbon black (CB) and high density polyethylene was used as core material, working as an inner electrode. A force sensor consisting of a number of fibers embedded in a soft CB/polyolefin elastomer matrix was manufactured for characterization. The fibers showed a clear piezoelectric effect, with a voltage output (peak-to-peak) of up to 40 mV under lateral compression. This continuous all-polymer piezoelectric fiber introduces new possibilities toward minimal single fiber sensors as well as large area sensors produced in standard industrial weaving machines.